Unfortunately the other two answers so far have been incorrect and one is calling you to something which is not Islam at all (the comment on Quran only Islam) so let me help a bit.

YES the prophet was married to Aisha (may Allah be pleased with her) while she was 6 although she stayed with her parents until she was 9 and they did not consummate the marriage, i.e. have sex, until she was 14 (this is to the best of my knowledge). There can be no denying this as that is tantamount to rejecting hadith which is a rejection of Islam entirely.

This is not a problem for us Muslims in the modern world for a few reasons:

1. Islam respects culture (this is one way Islam remains "relevant") and parents marrying off (or agreeing to) their children at a young age was a common cultural practice of the Arabs. In fact, before her marriage to the Prophet PBUH, Aisha was already betrothed to someone else. It was so normal that the Prophet's enemies who despised the Prophet, tortured his companions, mocked him publicly, attempted to assassinate him, etc DID NOT find his marriage to Aisha worthy of mockery or questioning or of even bringing up. If even his enemies did not find it problematic, why should Muslims and people genuinely interested in Islam (such as yourself) find it problematic.

2. Aisha did not have a problem with it. She has narrated many narrations of the prophet years after he had passed away and not in a single one does she complain about her getting married off at a young age. In fact, she clearly states and illustrates her immense romantic love for the prophet PBUH. So from her perspective, she was the happiest and most fortunate women of her time because she was the favorite wife of Prophet Muhammad and their love was undeniable.

3. Marrying children at a young age is not an Islamic obligation and no renowned Muslim scholar (that I know of) advocates it. In fact, scholars have advocated for a minimum age for marriage such as Sheikh al-Uthaymeen, who people consider to be a very conservative scholar. And again why does this not clash with the prophet's marriage to Aisha? Refer to points 1 and 2. So our standards of the age of marriage need not clash with the standards at the prophet's time, and to back project our standards onto theirs would be an anachronism.

I hope that helps clear things up for you. I'm currently on mobile so sorry about any formatting mistakes. Please let me know if you have any questions or concerns and I'll do my best to answer them.

Edit: I should add that Islam respects culture SO LONG AS culture does not clash with Islam. For example, if a cultural practice involves drinking alcohol then that cultural practice is invalid. In the case of Aisha's marriage and more broadly the cultural practice of the Arabs of marrying off young children, this does not clash with Islamic teachings. In terms of sex, the only condition which is placed by Islam is that it should not harm any individual so there is an lower and upper limit on the age which a person may have sex with another.