In Axis and Allies, do infantry units start at the industrial complex or anywhere I want?
No.  New units can only be placed at industrial complexes.

From the rules, page 21, "Action Sequence 5 - Place New Units On Gameboard":

Place newly purchased land units and air units in territories where you have owned
industrial complexes since the beginning of your turn-not in just-captured territories
with industrial complexes.


Furthermore

Any units that cannot be placed in industrial complexes are lost and put back in the tray.


Rules: https://www.wizards.com/avalonhill/rules/axis.pdf