Do they let prisoners out of jail before prison sentence begins?

In rare occasions they do.  If the defendant is looking at 180 months, the presumption is that he/she should be taken into custody after the change of plea hearing or guilty verdict at trial.  18 U.S.C. Section 3142.  However, if the defendant has done a good job while on pretrial release, adhering to the rules set for him/her by the Court, the presumption of detention pending sentencing can be overcome.  It is a tough argument to make because a 180 month sentence, in the eyes of the Government and the Court, provides strong incentive to flee the jurisdiction.  This is particularly true if the defendant is facing deportation after release from custody.  I recently kept an individual out of custody on a presumptive detain citing good work history on pretrial release, adherence to the rules of his halfway house and COVID concerns in the jail.  I had a good AUSA though.  It helps if they don't push back too hard.