Travel by land to Mexico and return to the US

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I am holding the visa waiver B2, this was on the emergency waiver (valid to enter the US but I am not sure if this can be seen as a real visa) as I arrived a month earlier for my H1B. One of the possible ways now is to travel to the Mexico to end that waiver and return with my H1B 10 days prior to my starting date. Changing of status takes a long time and it is not suitable for my case.

Has anyone had experience on travelling back and forth Mexico and US by land? For non-citizen and/or waiving program. I see that Covid test is also not mandatory when coming to Mexico or US by land, is that right? What I have is the H1B visa in hand, ready to be activated soonest at 1 Jan, I will come to the Mexico at some time around then. Do you foresee any problems for this travel?

This is my very first time involved in this border situation so I really need your help,

Thank you very much!