Mechanized infantry - you mean robomen; stormtroopers specially manufactured in Ludendorff’s secret underground lair.
You don’t need mechanized infantry - troops moved by train.
American Upgrade
The US had no heavy weapons industry - all the steel helmets, artillery, planes and tanks used by the Americans in Europe were supplied by France and Britain, who also helped to train US troops.
Therefore:
American cannot manufacture tanks, planes or artillery.
Instead
At the start of its turn, America can buy the 3 heavy weapon types - place the appropriate units in the mob zone. The cost is the difference in unit price over infantry, so tanks and planes cost 3 IPCs, artillery 1 - payed to the bank.
At the end of its turn the US can upgrade infantry units to the appropriate model.
The units concerned must be in an uncontested land tt in or adjacent to London or Paris, and that capital must be allied held.
If it is not possible to make an upgrade for lack of qualifying infantry, the purchased unit is lost with no refund.