According to the Pshat of the story and the Midrash (Avos d'Rabbi Nathan 1,8), G-d judged Adam and Eve straight away after they sinned and expelled them from Eden:
"...תשיעית הכניסו לגן עדן.
עשירית צוהו.
אחד עשר סרח.
שתים עשר נטרד והלך לו."
Why wasn't Adam given a chance to repent maybe till the end of the day, Motze Shabbos, or a month?
The standard answer is Midrash Bereshis Rabba 19:22
“The man said: The woman whom You gave…” – that is what is written: “I would speak, and I would not fear Him; for it is not so that I am, with myself [imadi]” (Job 9:35) – I am unlike the one who said: “The woman whom You gave to me [imadi]…” He heeded his wife’s words, but I did not heed my wife’s words. Rabbi Abba bar Kahana said: Dina was Job’s wife. That is why he said to her: “You are speaking as one of the disgusting women [nevalot] would speak. Shall we accept the good from God, [and not accept the bad]?” (Job 2:10). “Shall I accept,” is not written here, but rather, “shall we accept [nekabel]” – should we be pleased with the good but not be pleased with the bad? That was a rhetorical question. “With all this, Job did not sin with his lips” (Job 2:10) – [the implication is:] with his lips he did not sin, but in his heart he did sin].
Rabbi Abba bar Kahana said: “And I ate [veakhalti]” is not written here, but rather, “vaokhel” – I ate and I will eat again.
Rabbi Shimon ben Lakish said: Adam the first man was banished only after he blasphemed and spoke sacrilegiously. That is what is written: “He hoped to produce grapes, but it produced sour grapes” (Isaiah 5:2). “The Lord God said to the woman: What is this you have done? The woman said: The serpent enticed me, and I ate” (Genesis 3:13). “The woman said: The serpent enticed me [hishiani], and I ate” – [hishiani has three meanings:] It enticed me, it brought liability upon me, and it misled me. It enticed me, as it says: “The enemy will not entice [yashi] you” (Psalms 89:23). It brought liability upon me, as it says: “When you lend [tashe] to your neighbor” (Deuteronomy 24:10). It misled me, as it says: “Now, do not allow Hezekiah to mislead [yashi] you” (II Chronicles 32:15).
In other words, in his heart he wanted to continue sinning regardless. We also know that Adam simply accepted his punishment and did not realize that he can repent, Bereshis Rabba 22:13
“Cain departed [vayetze] from the presence of the Lord, and lived in the land of Nod, east of Eden” (Genesis 4:16). “Cain departed from the presence of the Lord” – from where did he depart? Rabbi Yudan said in the name of Rabbi Aivu: He cast the words behind him and departed, as though deceiving the Most High. Rabbi Berekhya said in the name of Rabbi Elazar ben Rabbi Shimon: He departed as one who shows a split hoof, and as one who deceives his Creator. Rabbi Ḥama said in the name of Rabbi Ḥanina bar Rabbi Yitzḥak: He departed joyfully, just as it says: “Here he is going out [yotze] to meet you [and he will see you and he will rejoice in his heart]” (Exodus 4:14). Adam the first man encountered him. He said to him: ‘What became of your sentence?’ He said to him: ‘I repented and reached a settlement.’ Adam the first man began beating himself on the face, saying: ‘Such is the power of repentance, and I did not know.’ Immediately, Adam the first man stood and said: “A psalm, a song for the Shabbat day…” (Psalms 92:1). Rabbi Levi said: Adam the first man said this Psalm, but it was forgotten from his generation, and Moses came and reintroduced it in his own name: “A psalm, a song for the Shabbat day. It is good to give thanks [lehodot] to the Lord…” (Psalms 92:1–2).
I guess a better question is how come Adam did not realize that he could try doing teshuva, why such an idea remained hidden for 130 years? Perhaps it should be related to the nature of his sin. Or perhaps if Adam knew that he could repent before the sin, Hashem would not let him repent at all as in Mishna Yoma 8:9:
With regard to one who says: I will sin and then I will repent, I will sin and I will repent, Heaven does not provide him the opportunity to repent, and he will remain a sinner all his days.
The alternative answer is discussed here.
