Can accidentally taking 2 birth control pills in one day cause you to start your period early?

No, it wouldn't. Taking the "mini pill" or Progesterone only (POP) BCP - missing one pill is enough to allow ovulation - which could cause pregnancy.

In a combination pill you have to miss 3 or more pills in a cycle for ovulation to happen. Going period free is a side effect of many BCP.

If you have been on the pill for over 6 months and this is the only period you have ever missed - taking a pregnancy test to reassure yourself wouldn't hurt anything.