The hardest bit is often the ten seconds before you join. You imagine everybody stopping, noticing you arrived and waiting for you to say something clever. Most of the time they are still talking about the game.
Join while something is already happening.
A scheduled gaming session is easier than entering a random general voice channel. The game gives everybody a shared reason to be there and gives you obvious things to say.
Start with information: "Where are we going?" "Do you need one more?" "I have not played this map much." You do not need an opening monologue.
Remove the technical anxiety first.
Do a microphone test before you join. Set the input device. Check your volume. Then stop touching the settings.
If you need one simple headset for both audio and voice, the Arctis Nova 1 (affiliate link) on Amazon keeps the setup straightforward without needing a separate microphone.
Do not buy a streaming setup because you feel self-conscious.
If your current headphones are good and the microphone is genuinely the only weak point, a small USB mic such as the HyperX SoloCast (affiliate link) on Amazon is enough. A boom arm, mixer and studio microphone will not make the social bit less awkward.
Give yourself one repeatable goal.
Say hello. Make one game-related comment. Stay for one match. That is a successful first voice session.
Do it again with some of the same people and suddenly you are not joining strangers. You are joining usernames you recognise.