Well, ignoring Paimon means that you will need to play with bugs, otherwise you don't have a lot of things to do.
You could ignore Paimon, and go straight to Mondstadt, but without reacting with Paimon, you could said that the time stops running, you will never meet with Amber and other characters.
Let's call this playstyle "no paimon" for short in this answer.
In "no paimon", you can't play with other people, other people can't join your world, and you can't join their world too. You can't glide using wings, no wings because you never meet Amber(okay, "no paimon" can use the boat in Golden Apple Archipelago and Inazuma to glide a little bit when you get out of the boat.) You can't open the event page, except in the Energy Amplifier Initiation event, it opens the event page after chatting with the NPC for once, and it bring flame to "no paimon" playstyle like what Prometheus does（Well， that requires some usage of bug to get to Spiral Abyss). Also, you can't open mails, which means "no paimon" can't get the free 5 star character.
Your main character can't use any element in this playstyle, and you can't get any other character except Xiangling by using bug to get to Spiral Abyss first(in earlier version, now the bug is fixed.), and complete 3-3, then, you need to have a teleport waypoint outside of the red circle(by using bug in earlier version, fixed too.), and that waypoint has to be able to get to the NPC of Energy Amplifier Initiation event with the paimon by your side saying that "How about we explore the area ahead of us later" and control your character moving to inside the red circle.
Primogem almost worth nothing in "no paimon", you can't wish at all. The only usage of the primogem is that you could use primogem to buy some level of battle pass.(You can't buy Genesis Crystal, but you could buy battle pass.) Maybe you will say that primogem can buy Original Resin, but Original Resin worth nothing before you have Xiangling, Xiangling effect the "no paimon" playstyle greatly.
Before you get Xiangling, “no paimon" can't get over 25 in Adventure level, means no 5 star Artifact, even 4 star Artifact are very rare too. Also, character level is lock on 50. It is because the Electro Hypostasis in the world level upgrade mission, you don't have any element to destroy Electro prisms to kill the Electro Hypostasis. But with Xiangling, Electro Hypostasis is killable, and means that the adventure level can get over 25 now.
After all, "no paimon" is not that playable right now, you can't get Xiangling now, so no way to bypass Adventure level 25 now, and no waypoints outside the red circle too, those all need bugs, and the bugs is all fixed right now. And you could see that "no paimon" is a playstyle that is focused on fighting with programmer(XD).