You should do it as soon as you can. On your Twitter dashboard, click on the following:
Settings and Support » Settings and Privacy » Your account » Download an archive of your data
I say this because it can take up to 24 hours for Twitter to compile all your stuff and send it to you, and if you're anything like me, you want to make sure every meme and shitpost you've ever written since 2008 finds a safe space on your hard drive next to your porn folder you named "homework".
I made a Mastodon profile, if that's your thing.
It's actually kinda been fun looking at some of these old Tweets. Fourteen years ago, I was still doing the exact same thing I do now: post outdated memes.

This other one made me smile. I was talking about a girl I just met in one of my classes in college:

Fast forward to today: We have a child together 😄