Can a sin be too big for Allah to forgive?

No, no sin is too big for Allah to forgive if you turn back to Him sincerely while you are alive. The only sin Allah does not forgive is dying while still worshipping others alongside Him. Even that door stays open until death, which is why accepting Islam wipes the slate clean. Despair of His mercy is more dangerous than the sin itself.

Allah's mercy is bigger than any sin

The Quran speaks directly to people who feel they have gone too far:

۞ قُلْ يَـٰعِبَادِىَ ٱلَّذِينَ أَسْرَفُوا۟ عَلَىٰٓ أَنفُسِهِمْ لَا تَقْنَطُوا۟ مِن رَّحْمَةِ ٱللَّهِ ۚ إِنَّ ٱللَّهَ يَغْفِرُ ٱلذُّنُوبَ جَمِيعًا ۚ إِنَّهُۥ هُوَ ٱلْغَفُورُ ٱلرَّحِيمُ "Say, 'O My servants who have exceeded the limits against their souls! Do not lose hope in Allah's mercy, for Allah certainly forgives all sins. He is indeed the All-Forgiving, Most Merciful.'" Quran 39:53

The Prophet ﷺ related that Allah says: "O son of Adam, if you came to Me with sins nearly as great as the earth, and then you met Me not associating anything with Me, I would come to you with forgiveness nearly as great as it" (Jami at-Tirmidhi 3540).

Even a person who killed 99 people

The Prophet ﷺ told of a man among earlier peoples who had killed ninety-nine people and then sought a way to repent. He was told his repentance could be accepted, he set out toward a righteous land, and died on the way, and the angels of mercy took him (Sahih al-Bukhari 3470). The story shows how wide Allah's mercy is. It does not cancel the rights of victims, which still matter. See Does Allah forgive sins against other people?

The one exception

The Quran says: "Allah does not forgive associating others with Him, but forgives anything else of whoever He wills" (Quran 4:48). Scholars explain that this refers to a person who dies upon shirk without repenting. A person who is alive can still repent from shirk, which is exactly what happens when someone says the shahada. See Are all my sins forgiven when I become Muslim?

Despair is the real danger

Satan wants you to believe you are beyond help, so you stop trying. The Quran says, "Who would despair of the mercy of their Lord except the misguided?" (Quran 15:56). A person who commits a serious sin and feels deep regret has not lost faith. That regret is a sign of a living heart.

What to do if you feel your sin is too big

Stop the sin and turn to Allah today. Do not wait until you feel "worthy".
Ask for forgiveness sincerely and make a firm intention not to return. See What are the conditions of tawbah?
Put right anything you owe to other people.
Follow bad deeds with good ones. The Quran promises that Allah will change the evil deeds of those who repent, believe and do good "into good deeds" (Quran 25:70).
If you slip again, repent again. Allah's mercy does not run out.

Because mercy is so wide, a Muslim should not use it as an excuse to keep sinning. Hope and healthy fear go together. See Will Allah forgive me if I keep committing the same sin?

Key points

No sin is beyond Allah's forgiveness for a person who repents before death.
The exception is dying upon shirk without repentance (Quran 4:48).
Despair of Allah's mercy is itself a serious mistake.
Repent sincerely, return people's rights and follow with good deeds.

Tip: If guilt over a past sin keeps you from praying, pray anyway. Prayer is part of the cure. For ongoing feelings of hopelessness, also talk to a trusted imam or counsellor.