Anyone knows how to do that? Instead of opening up the bot. The message will just load in the background first, so that when the bot is clicked, the message will already be there.

You can’t do that as of now, it will send the message after the bot is opened.

Which task card is the one to use for automatically initiating the conversation once the user opens the chatbot?

Just select trigger "Conversation Started" and connect with first node

This trigger will only work if the bot is opened, not on page load

I don't have any triggers under Events