Is it possible to make alacritty starts with tmux?

Yes. In the shell option, you can set the program you want to run and even pass in the arguments. For example, in your alacritty.yml file, you can set this:

shell:
  program: /usr/local/bin/tmux # <- set this to the path of your tmux installation
  args:
    - new-session
    - -A
    - -D
    - -s
    - main

Every time you start alacritty, tmux will start a new session and pass the other args.

Or go the easy route and launch your terminal this way:

alacritty -e tmux

i'm using this script: https://cedaei.com/posts/ideas-from-my-dev-setup-always-tmux/ had it from https://lobste.rs/s/n5blid/ideas_from_my_development_setup_always

and use it in alacritty as:

shell:
  program: /home/user/.local/bin/tmux_chooser.sh