The US did not fake the Gulf of Tonkin Incident. The truth is far more complex than that.

This is what I wrote the last time this came up:

Neither of the reports were fabricated.

What we have to understand is that incorrect judgements or reading of situations are very common in conflict situation and confusion, 'the fog of war', is very present. The first attack, on the 2nd of August, was an attack that actually did happen and has been confirmed by the North Vietnamese, among them General Vo Nguyen Giap. The second, on August 4th, did not occur. While it was reported (and this report handed to President Johnson), it was later retracted by the man in command. Johnson was uncertain about the second attack but chose to act on the event as a whole.

The truth is that Johnson took advantage of the Gulf of Tonkin to further his policy in Vietnam and did so not knowing the complete story or having accurate information at his disposal. But the decision was made 30 minutes after the second alleged attack and reports were conflicting over the next few days, days that were already critical in making the decision.

/u/ThinMountainAir added an excellent addition to this by describing just how muddled the intelligence situation was at the time.