This might be the Time Riders series by Alex Scarrow. In that, three teens were recruited by being snatched out of time just before they would have died. Their headquarters is some abandoned rooms under a bridge, and the headquarters deliberately time loops over two days (so that there is less chance of its existence being discovered). The fifth book in the series is "Gates of Rome" in which the team is stranded in ancient Rome, and an alternate timeline comes into existence where the Romans have access to future technology.

This might be the Time Riders series by Alex Scarrow. In that, three teens were recruited by being snatched out of time just before they would have died. Their headquarters is some abandoned rooms under a bridge, and the headquarters deliberately time loops over two days (so that there is less chance of its existence being discovered). The fifth book in the series is "Gates of Rome" in which the team is stranded in ancient Rome, and an alternate timeline comes into existence where the Romans have access to future technology. The series was published between 2010 and 2013.