Wave 3 is your best bet
Try get one in cart wave 1. Keep the browser tab up, complete purchase at start of next wave.
You can use a browser bot to refresh the cart page with the Javelin every few minutes. Using a bot was working in 2020, not working in 2021, but working again in 2022. Don't forget to turn off the bot before next wave ;)
In 2020 you could still buy the ship using the direct link from the standalone ship page filtered to Javelin. That's how I got mine and a Kraken.
In 2021 they prevented that, making that link not working and forcing people to go through the IAE page (no other means worked then, not through the pledge store or the ship page in the matrix, untill after a few minutes of wave start). I only got a Hull-E and Phoenix that year because of that. Having a limited item in cart from previous wave was also not working.
2022 it seems they went back to the old system for Invictus, got additional Kraken this way.
So get ready with multiple browser tabs (or multiple computers/smartphone). Tab with IAE page, tab with standalone ship page filtered to Javelin, tab with standalone ship page sorted with most expensive ship first, tab with page from ship matrix which will show purchase options when wave hit.
And Lefty got 2 Javelin this way, why 2 javs, ask him, he probably wants to catch up with Ecstasy