Congratulations on your admits! I am afraid it may be too late.... not impossible but very tight. The first thing I would check is the Embassy Waiting times and how long it will take to get the visa processed.
Also, you should immediately (monday morning) ask the school what would they do if you are a few weeks late? What would happen then? Would they let you defer or you would start late or ??? They clearly have had situations like this - what is their expectation?
As to the situation in case you are late, there are about 2 weeks of orientations that take place before school. This time is fairly useful as you get to meet your classmates, get to know about the basics, usually do some kind of a trip or a retreat or team-building exercises. It would be a bummer to miss these but if you have to miss them, you would not be missing classes at least.... but you will have to change all your plans for housing/apartment/city, etc.
This is very late in the process.... are you mentally prepared to change?
Of course if there is a better rank and scholarship involved, it may be well worth the hassle and potentially risk. The only person I know who was in such situation was Souvik who got admitted to Sloan from WL late and he let it go, and did not switch from Ross to Sloan. He was happy with that decision.
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