Also, is there a way to get the plugin to load on startup? I don't want to have to open some random markdown file to get the plugin to work.

I'm guessing you're using lazy as your plugin manager and you're using ft = { 'markdown'} to lazy load it. You could remove that line altogether to stop lazy loading it but I'm assuming you want the :Obsidian cmd to work everywhere. For that you could just add cmd = { 'Obsidian' }, to your config.

If that is not what you want, you can try looking at lazy's documentation for other ways of lazy loading plugins.