Înaintea mea can mean physically (as in front of me or ahead of me in a queue) as well as in time (to happen before me).
În fața mea lacks the temporal sense.
I think a safer translation for Nu este nimeni înaintea mea! would be There is nobody before/ahead of me! instead of There is nobody in front of me! as it would also cover the temporal sense.
I know that it's just a typo, but for other people who might come across this, "raţa mea" actually means "my duck," while "în faţa mea" means "in front of me."