Yes, Canon T100/4000D is compatible with EF 75-300. And if you want to reach 400mm for this sensor you will have it because equivalent focal length of this lens on this body is 480mm.
But you may have challenge with autofocus which may not work on long focal lengths (on this camera it will work fine till f5.6)
If you want to reach 400mm (real value) IMHO there is no cheap way. Maybe you can use mirror lens but they are manual focus and there is probability the image quality will not make you happy.