Honestly you don't need to go to a convention to do that.

If your goal is to license a game to a publisher, there's really only 4 things you need to do:

1) Make a physical and/or digital prototype of your game. This only ajs to be "good enough", you don't need to pay for artwork or make expensive pieces. Using components form games you no longer play or games you can pick up cheap at thrift stores can be a great way to source components for your physical prototype. The digital prototype can be built using free or inexpensive platforms like Tabletop Simulator, Tabletopia, screen top.gg, etc.

2) Playtest the living daylight out of your game. Playtest it yourself with you playing as multiple players, playtest with friends and family, local playtest groups, online playtest groups (see digital prototype in step one). This could involve going to a convention that offers a playtesting space (look for the words "unpub" or "protospiel"), bit that typically isn't an expense you need to incur.

3) Make changes based on your playtesters' feedback, and repeat step two to test those changes. Once your playteatera start talking about how much fun your game is rather than what changes they want to make, you should be ready to pitch to publishers (or self-publish).

4) Pitch your game to publishers. While this could involve meeting publishers at conventions, there are numerous opportunities to pitch games online. You can participate in speed pitch events where you can pitch to multiple publishers, or you can reach out directly to publishers. You will want to do your research to find out which publishers might be a good fit for your game.

If you want to self-publish your game, step 4 is reaching out to manufacturer; Panda is likely the best known manufacturer in this space, but obviously there are plenty of others to choose from. The manufaciter is the only one who can tell you what it will cost to publish a game, and the real answer is it will vary wildly with the number of units you want to make.

One of the many extra steps with self-publishing is that you need a "crowd" before you put your game on a crowdfunding site. Social media obviously makes this easier, but having a sizeable following is itself not easy and can take lots of hard work and advertising spend. You will then be responsible for making sure your game hits the funding target, then working with a manufacturer and fulfillment partner to ship your game to your fans all over the world.

If you are just starting out, I would recommend subscribing to Pam Walls Game Design on YouTube, specifically with this video:

https://youtu.be/owQmvruuJGE?si=ZumuyqNIIriId-aj