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Your best bet is applying for internships at mid-tier firms. Once you get in, make friends with the associates/ senior-associates. They will move to other places by the time you graduate. So you will have some connects at various law firms by the time you graduate.
Apply well in advance to tier 2/3 firms.
You will face lot of rejections. Many won't reply. But that shouldn't stop you from trying.

Meanwhile, read, write and repeat.

There's still time. You will be fine.