Short Answer: No, fairly certain you cannot (not the border wall anyway).
Long Answer: I don't think this is about the Spanish Mexican mixed people but the native Mexicans before any European influence happened. Not only is there no USA because Europeans haven't discovered it. But they probably own southern Texas during this time period and are already across the border defeating the point of a wall there even if you could build one.
Concession: I don't know if other walls might need to be built for other reasons.
Disclaimer: I don't actually care about the political context before anyone asks, I'm factually answering OP because Rick is the one asking.
Long Answer: I don't think this is about the Spanish Mexican mixed people but the native Mexicans before any European influence happened. Not only is there no USA because Europeans haven't discovered it. But they probably own southern Texas during this time period and are already across the border defeating the point of a wall there even if you could build one.
Concession: I don't know if other walls might need to be built for other reasons.
Disclaimer: I don't actually care about the political context before anyone asks, I'm factually answering OP because Rick is the one asking.