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It is explained in the Bhagavad Gita that every life is governed by deeds and actions from past life which is why some people are blessed with a silver spoon in their mouth while some suffer, which means life is pretty much predetermined. Now how will the life be determined for people in their very first birth since they have no previous birth to derive from ?

You said:

Now how will the life be determined for people in their very first birth since they have no previous birth to derive from ?

Actually, your answer lies very much in the Bhagavad-Gita itself. There is no such thing as "first birth" for a Jiva. "First birth" implies souls are created but that is not the case since every Jiva has always existed just as Bhagavan has always existed. Krishna Himself states this explicitly in the Bhagavad Gita:

It is not at all that once I did not exist, nor (that) you, nor that all these kings (did not exist at anytime). And surely it is not that all of us shall not be existing hereafter. (Bhagavad-Gita 2.12)

Sripad Ramanujacharya has tried to rearrange these words to make it more easier to comprehend in his commentary on this verse:

I, who am, as you know, the Lord of all, in beginningless time prior to this present, did not cease to exist, that is, did certainly exist. It is not that these embodied souls like you, who are subject to (My) control, did not exist, that is, I and you, "hereafter" that is, after the present time, shall not be existing. We shall (all) be certainly existing. Even as there is no doubt in regard to the fact that I, the Supreme Self and the Lord of all, am eternal in the same manner you (i.e. you, Arjuna and these) who are (all) embodied individual souls, are also seemed to be eternal...

Later, in Bhagavad Gita 2.20, Krishna Himself again stress on the eternal nature of the soul:

Neither is this (Self) ever born, nor does (it) ever die. It cannot be that it (i.e. this Self), having been in existence (in the past), will not be in existence again (in the future). This (Self) which is unborn, eternal, constant and ancient (as well as new), is not slain when the body is slain. (Bhagavad-Gita 2.20)

So to sum it up, there is no such thing as "first birth" for any individual jiva. Souls are never created, just like Bhagavan is never created. Bhagavan and individual Jivatmas has always existed and will be also remain to do so.

According to Sri Krishna, we are born out of the Avyakta and again with death merge with the Avyakta(Gita 2/28):

O descendant of Bharata, all beings remain unmanifest in the beginning;; they become manifest in the middle. After death they certainly become unmanifest. What lamentation can there be with regard to them? (Translation by swami Gambhirananda)

This whole creation or Maya is known to be 'Anadi' ie without any beginning.

Sri Krishna says to Arjuna (Gita, 4/5)

[The Blessed Lord said O Arjuna,] many lives of Mine have passed, and so have yours. I know them all, (but) you know not, O scorcher of enemies!

He however assures all by saying (Gita, 7/14):

Since this divine Maya of Mine which is constituted by the gunas is difficult to cross over, (therefore) those who take refuge in Me alone cross over this Maya.

(All translations by Swami Gambhirananda)

Now how will the life be determined for people in their very first birth since they have no previous birth to derive from ?

According to Vedanta, there is no first birth. The Jivatma has no beginning in the cycle of life and death.

The great Vedantic philosopher Rāmānujāchārya has stated in his work Vedartha Sangraha, or "summary of the meaning of the Vedas," the following:

The crown of Vedas i.e., The Upanishads, which lays down the good of
the whole world, enshrines this truth: A seeker, after first acquiring
a true understanding of the individual self and the Supreme and
equipped with the performance of the duties pertaining to his station
in life, must devote himself to the meditation, worship and adoring
salutation of the blessed feet of the supreme Person. This done with
immeasurable joy leads to the attainment of the Supreme.

The
individual self is subject to beginningless nescience, which has
brought about an accumulation of karma, of the nature of both merit
and demerit. The flood of such karma causes his entry into four kinds
of bodies — heavenly, human, animal and plant beginning with that of
Brahma downwards. This ingression into bodies produces the delusion of
identity with those respective bodies (and the consequent attachments
and aversions). This delusion inevitably brings about all the fears
inherent in the state of worldly existence. The entire body of Vedanta
aims at the annihilation of these fears.......

The [Brahma Sutra] aphorisms connected with this issue are, ‘Partiality and cruelty
are not to be ascribed to Brahman, because of the dependence on
karma’, and ‘If it be said, “There is no karma, as there was no
differentiation” we deny that supposition on the ground of
beginninglessness; it is reasonable and so found in actuality
(B.S. 2;1:35-36)’.

The Brahma Sutras, written by Rishi Vedavyasa, themselves state that the Jivatma has no beginning in samsara; there was no "first birth."

2.1.34 - Not inequality and cruelty, on account of there being regard; for so (Scripture) declares.

2.1.35 - If it be said 'not so, on account of non-distinction of deeds'; we say, 'not so, on account of beginninglessness'; this is reasonable, and it is also observed.

Ramanujacharya's commentary for Sutra 2.1.35:

But before creation the individual souls do not exist; since Scripture
teaches non-distinction 'Being only this was in the beginning.' And as
then the souls do not exist, no karman can exist, and it cannot
therefore be said that the inequality of creation depends on
karman.--Of this objection the Sûtra disposes by saying 'on account of
beginninglessness,' i.e. although the individual souls and their deeds
form an eternal stream, without a beginning, yet non-distinction of
them 'is reasonable' (i.e. may reasonably be asserted) in so far as,
previous to creation, the substance of the souls abides in a very
subtle condition, destitute of names and forms, and thus incapable of
being designated as something apart from Brahman, although in reality
then also they constitute Brahman's body only. If it were not admitted
(that the distinctions in the new creation are due to karman), it
would moreover follow that souls are requited for what they have not
done, and not requited for what they have done. The fact of the souls
being without a beginning is observed, viz., to be stated in
Scripture,'The intelligent one is not born and dies not' (Ka. Up. I,
2, 18); so also the fact of the flow of creation going on from all
eternity, 'As the creator formed sun and moon formerly.' Moreover, the
text, 'Now all this was then undeveloped. It became developed by form
and name' (Bri. Up. I, 4, 7), states merely that the names and forms
of the souls were developed, and this shows that the souls themselves
existed from the beginning. Smriti also says, 'Dost thou know both
Prakriti and the soul to be without beginning?' (Bha. Gî. XIII,
19.)--As Brahman thus differs in nature from everything else, possesses all powers, has no other motive than sport, and arranges the
diversity of the creation in accordance with the different karman of
the individual souls, Brahman alone can be the universal cause.

Summary

The Jivatma is eternal (was never created), and has always been in Samsara. According to the Vedas, the Jivatma takes birth in a body according to it's karma done in previous bodies. This implies that the soul has no first birth.