When I was in grad school (25+ years ago, but I think this still applies), I got nothing my first semester when I started in the fall. But a couple of TA positions opened up in December for the spring semester and they offered one to me because I had previously expressed interest. So even if you don’t get something to start with, it’s possible to get something later. Once I had that TAship, I was offered another one for the subsequent semester (I declined because by then I had an RAship lined up, but once you get an assistantship and do well it seems easier to continue getting offers after that).
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