OTL the American navy had roughly a dozen first class ships (large steam frigates, not ships of the line) against the Mexican total of zero. (That's right; zero. The Mexican economy was such a basket case that they could not afford even one warship.)
To reach the totals given in the OP would require the Americans to roughly double the size of their fleet, which is certainly within the realm of possibility, given that the Union went from fifteen ships in 1861 to over 600 in 1865. American ships of the period were generally well equipped, well maintained, and well supplied, with well trained crews and officers; I expect the same would hold true for this fleet.
On the other hand to get a fleet that size the Mexicans will have to buy, beg, borrow, or steal every ship they can lay hands on; the result will be a hodgepodge of different ships armed with every conceivable size and shape of naval gun, crewed by whoever they can persuade or coerce into serving aboard this misbegotten fleet. Given that they have virtually no one with any sort of naval experience available any training is going to be rudimentary and uneven.
With this sort of disparity an American victory is almost a certainty and any Mexican who survives the engagement should count himself among the most fortunate of individuals.
I grant that this is not the only possible outcome, but it is the most probable; a Mexican victory in such a battle would be the upset of the century.
If we are talking about OTL, I'd agree with you. But I would argue that it would be impossible for OTL Mexico to put together a fleet of the size specified in the OP. Therefore, the OP must, perforce, be assuming an ATL Mexico which has a much better economy. Therefore any assumptions we are making from OTL are simply not useful in this scenario. For all we know, this ATL rich Mexico had their ships built and equipped in England to RN standards and their crews trained by RN officers.