The rest of the party is involved because the whole party is close enough together for the scene
The leopard beat the best passive perception in the party, he is hidden from them all.
Initiative determines the order of combat and the party is surprised by combat starting. They all roll initiative with disadvantage.
That all seems clear RAW for 5e 24.
The big question is what happens for anybody who beat the leopard's initiative when their first turn comes up. I now see three main options.
1 They do not know anything is going on so they take no actions on their turn in the round. Initiative just determines order and as a DM I go to then skip everyone with a better roll and just start at the leopard's initiative then go from there. Narratively they did not notice the leopard until it does something. Getting a good roll might actually mean going after someone who gets a worse roll.
2 They sense something is up but do not know about the leopard specifically. They might dodge or whatever. I start with the highest initiative person and say what do you do? giving no indication about the leopard until it goes. Narratively they notice something on some level. Game level at the table they get some advantage from rolling high and there could be some neat tension from what do we do and the uncertainty of what is coming but knowing something is coming imminently.
3 They are in combat and won initiative, I lay down the combat mat and if they ask about the mini for the leopard I say it is the leopard they did not spot. If they attack the hidden leopard and I as DM think of it they get disadvantage on any such attack rolls because successfully hidden means invisible condition which imposes disadvantage on attacks against the invisible target RAW. Narratively they notice something specifically about the leopard, though it is still mechanically hidden.