How do I get my first 100 users as a solo developer?

Short answer

Manually, one at a time, from places those people already gather. Find the five forums, subreddits, Discords or Slack groups where your users complain about the problem you solve, spend a fortnight being genuinely useful in them without linking anything, then tell people what you built. A hundred users is small enough that it does not require a growth strategy — it requires roughly a hundred conversations.