U.S. trademark law unequivocally holds that first use of a mark in commerce is the sine qua non of registration. If someone has already trademarked the logo, then you cannot do similarly. There is one possible exception.
If you purchased the logo and you were granted an exclusive copyright license to use the logo by the vendor, then you could prevent your competitor from using the logo, because while the competitor could stop you from using the logo in commerce, you can stop the competitor from using the logo for anything and everything.
That said, the biggest problem here is that, unless your competitor is actually shipping product into the USA, then you wouldn't have much leverage over the competitor, as Mexico courts are pretty useless political organs, and unless you're prepared to bribe everyone in the government involved in determining your rights, the competitor is likely to simply ignore you.
On the other hand, if the competitor is shipping into the USA in quantity, and if you have an exclusive license over the copyright, then you can get a court order to seize all of the product in the USA, and thereby hopefully, force a settlement.
The cost-effective solution is probably to develop a new logo by hiring a logo design company in the USA to produce something for you from scratch. That's the only way to really protect your rights. You have to have absolute control over the logo from the moment of creation.
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