Yup. Normal on all military rifles (M1, M14, m16) and commercial equivalents. The firing pin is not held back by a spring. It will travel forward with the bolt and may protrude slightly. Once it taps the primer it will stop and maybe bounce back a little. It doesn't (USUALLY) have enough force to ignite the primer.
Things to watch for to keep things safe:
On the gun side make sure the firing pin channel isn't gunked up to prevent the firing pin from moving back freely.
On the ammo side, ensure primers are seated correctly and have hard enough cups. Milspec primers have very hard cups whereas Federal primers are often known for having soft cups.
If the above are not followed, the primer may go off on bolt close (slamfire).