Dumpster Gang how to invite friends goes through your own Steam friends list, because the lobby is friends-only by design — there is no matchmaking, and up to four raccoons can play online together.
Dumpster Gang how to invite friends: a friends-only lobby
Asked about matchmaking and public lobbies, the developers said they talked about it during development and plan to stick with the friends-only lobby approach, because adding a matchmaker brings a lot of overhead and complexity. It is not planned for the full release, though it is not ruled out forever.
So there is no public game to join and no invite code to type. Your Steam friends list is the guest list. If you need players who are not your friends, the developers' answer is the game's Discord Looking For Group channel.
Whether a party can also be a party on one couch, or across PC and console, is a separate question, and the platform support guide covers both.
How many players can join
Up to four raccoons — you plus three friends — in online co-op, and the demo supports the full four.
The developers are currently tuning the experience around that cap of four and have said that increasing the party size may be looked into later depending on time, because the team is small and focused on the December release. Requests for a fifth player who plays as the Exterminator are on their radar but are not part of the December launch, so do not plan a run around playing John — the stealth guide covers the half of the game he controls.

Playing alone works
Yes — the developers state that the single-player experience is just as playable as the multiplayer one. A solo raccoon can complete the demo's missions, and a caught raccoon can get out of John's hands by itself, so a cage is only an inconvenience rather than a failed run.
It is simply harder. Nobody can distract John while you make the coffee, the same missions take longer, and players report that adding raccoons makes the game noticeably harder. The coffee objective guide has the solo timing that works best, and the stealth guide covers the noise problem that comes with doing it alone.