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I want to think that it was a series or a TV movie series. The movie/series looks like timeless but it not it well to what I have read in the episodes summary. It looks like a 2010s movie. I did not see the beginning of it, but it was about a team that went back in time to stop/kill a man because he was going to be part of a terrorist attack [I think, that's what I understood] or some kind of disaster.

It was a one white guy, a white woman, and a black man. If I'm not mistaken they go back in time to New York in the 1920s or 30s. They are in a lab with I think military help. They ended up landing in a basement, and they were able to still communicate with the present with some hearing aid. They take a car from a guy that works in an hotel. A dilemma comes up as they should have come earlier and they should have had like 7-8 hours to do the mission but because of some problem they have 4-5 hours.

They find the guy, they were about to kill him but realize that he has a little sister, they do research and find out that she dies later. The white guy tells the guy that he is an Angel and he knows what will happen, to not join the guys if not he will kill him, and to take care of his little sister. The people from the present tell them that the incident no longer happens. They barely make it back in time to come back to the present. One of the military or spy goes into the time machine and chaos breaks down. And that's all to it.

This was "Rewind" from 2013.

From Wikipedia:

The film opens with an apparent terrorist attack involving a nuclear
device which destroys New York City killing 9 million people. The
perpetrator, Benjamin Rourke, a Nobel prize winning physicist, had
become embittered by the death of his wife, and having learned that
there is a potential time travel experiment in progress, he engineers
the bomb plot to force the US Government to send agents back to
prevent the disaster happening. He had also arranged matters that the
only way to do this was to have them prevent his wife's death. The
story describes the process of the team, CIA agents Sean Knox and
Danny Gates, and scientist Lyndsay Bryce, arriving at this conclusion
and their efforts to achieve this without doing too much damage to the
time-line.

The Movie is as you described. They are going back in time to kill the man who murdered the "terrorist's" wife, years before he murdered her.

The time dilemma is the wormhole is unstable. It was supposed to take 7-8 hours to close. but not long after the team passes through it, the lab realize it will be closing sooner.