It sounds like the squatter would need to be evicted. This is something that your seller should take care of for you, as the hassle and expense should not be YOUR problem. That is especially true, if the seller allowed this to happen. I would not close until this is taken care of. Otherwise, this will be a problem that YOU inherit.
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The seller's anticipated failure to tender absolute possession to you at closing is a problem -- just like if you had discovered a problem during the inspection. Further, because you are aware of the squatter (it is not a problem being "hidden" from you) you need to use your bargaining power during the process of this sale to fix the problem, prior to closing, at which time it will be left up to you to deal with in court. You should demand that the sellers remove the squatter through a legal eviction process prior to, and as a condition of, closing.
This is a seller's legal problem, but a very practical concern for you considering your eminent move date. While it may be arguable that storing materials in a garage is not occupancy which requires eviction (because it may be considered a license or bailment scenario), that is an argument seller needs to make, not you. You will want to review with a legally advisor your purchase agreement with the seller to fully understand your rights should the seller not be in a position to close as promised.
Disclaimer: This response is for general information only and covers only broad legal concepts. In no way is this response intended as formal legal advice. If you have further questions regarding a legal matter, please consult a licensed attorney.