Some modern hosting services provide trial servers. For instance, Gaming4Free and LegionHosting often offer, or have offered, free trial hosting for the game LegionHosting Gaming4Free. Steam Family Sharing (If Available)
You can Sign Up for an account on the official website for free without buying the game.
: To download and update mods through the in-game manager or the official Mod Portal, you must have a verified account tied to a game purchase.
Because Factorio updates roughly every two weeks with bug fixes and content tweaks, any "free account" from three months ago is already useless for multiplayer. The game forces a version check. If your client doesn't match the server's version, you simply cannot play with friends.