Yes you can get through
The only place someone would need to crawl is at the very end past the official turn around point. You aren't supposed to go that far anyway. Before that point you would at most need to duck down for some low bridges. Those areas don't extend more than 5 to 10 feet at the most. I would encourage you to go!
The low sections just require bending over, not crawling. And you can turn around at anytime and go back, there's no necessity to go all the way to the end of the cave.
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