Don't really need a way of suppressing earlier-gen power levels. You're a neophyte that has massively powerful blood, not a 700 year old vampire with full knowledge of his abilities.
That's pretty much what I've been saying. Being a lower generation than someone is not the only way to resist dominate. Your character is just not powerful enough to resist, or by the PnP rules, your willpower is too low.
Of course, the fact that LaCroix can dominate you would make him 8th gen too, which is fairly low for an American prince. We know LaCroix only around 200 years old which would typically make him around 10th-11th gen IIRC. It's not completely out of line to think his sire was 7th gen, but I think it's more likely he engaged in diablerie before, maybe when he was traveling in Africa. It would certainly be in character.
The canon explanation is that the taxi driver is a Malkavian who thinks he's Caine, and working from that premise I think a reasonable argument can be made that he is the player's sire. The entire plot with the sarcophagus is implied to be his idea by Jack at the end, after all. Siring the player could have easily been part of that, and it certainly wouldn't be out of line with the kind of crazy convoluted plan a Malkavian would come up with.
I like the idea that the vampire who is executed in the opening cutscene was just a fall guy, maybe even dominated into believing he had embraced the player so it would be convincing. Otherwise, if he actually was 7th gen, I doubt LaCroix would have been able to execute him that easily, and there's no way he'd let the player live afterward - an 8th gen vampire is potentially a huge threat.
Edit: Eh, thinking about it again (and I have no idea how I missed this) that only makes sense if the player is also a Malkavian. I don't know of any way for a vampire to embrace a childer into another clan, except as a caitiff.