How can I verify the fair launch myself?

Use the open chain and open source. First, inspect the genesis block and confirm it contains no large insider balance. Second, read the early blocks and confirm each pays only the standard block reward. Third, reconcile circulating supply against mined blocks times the block reward; the numbers should match. Fourth, read the project documentation for any mention of allocation, sale, or treasury, of which there should be none. Fifth, cross-check with a second independent tool. If all of these line up, you have verified the fair launch yourself rather than trusting a press release.