So level 4 raids aren't a thing here but

It should be possible as long as the Machamp doesn't have Dynamic Punch. I made a DB/H Dragonite last night out of a DB/HB one I had left over and it's been great against boss Machamp. Have not successfully solo'ed one myself yet, but there are lots of claims to have done so on reddit.

For a Machamp raid you want psychic, flying, or fairy types. Taking in six Tyranitars against a Machamp would be a very bad idea.

Alakazam with Psycho Cut, Espeon, Exeggutor, Dragonite with Hurricane, Charizard with Air Slash, maybe Scyther with Air Slash/Aerial Ace, Possibly Crobat with Air Slash, maybe Clefable.

Yeah, several people claim to have soloed a level 3 Machamp.

I soloed a machamp so yes there is hope!
I used pure psychic counters though since I only have 1 Dnite that was at a gym at the time.

This was my lineup, all above 75% IV and with the lowest being lvl 31.5 and the highest being 34.5 (I'm lvl 33).
Espeon - confusion/psychic
Espeon -confusion/Psybeam
Alakazam -confusion/psychic
Alakazam -psycho cut/future sight
Exeggutor -confusion/psychic
Exeggutor -confusion/solar beam

I beat it with 10 seconds left and my last eggy was just under half hp. I was quite proud and so now I want to be able to solo all the lvl 3's. So I have team building to do!

I've tried twice with a Gengar boss, but got timed-out both tries. Went with Psychic types, but I guess I could had gone with a all line-up of Rhydons with Mud Shot or Slap/Earthquake.

I will say I had no trouble dodging it's Focus Blast on the second one. The Gengar would make a reaching movement, then the sound would play, then text would appear so I was able to dodge all of them.

There's a chance. However with 3mins to complete, it's pushing it. Most solo's I've seen and done you almost have to be perfect i.e. dodging (switch out before death animation cause it eats up time), and being effective in your dps. I haven't been successful because I always time out with the boss having 5-10% health left. Even against Vaperon (who's supposedly the easier of the Tier 3). Machamp in the same tier, my last raid against one I did with one other person, and we finished w/ plenty of time. But again solo, timed out with it 5% using Dnites between 3-3.4k DT/HU. Don't really have optimal Alakazams to use.

This is 1 matchup that a DT/Hu Dnite would be better than a DT/O one I think...

A side thought, I think Exeggutor with Solar Beam or uncharacteristically, Psychic, would also be a prime candidate. Weaker than Zam or Espeon sure, but I think the high DPS of Solar Beam over time even without stab may tip the balance. A Confusion Jynx is useful too but not sure if the charge moves are up to scratch.

Air Slash Charizard could also maybe get an honorable mention too.

Never tried the Solo Machamp but this is what I would go in with:
ZH/FS Espeon
PC/Psychic Alakazam
Confusion/Solar Exeggutor
DT/H Dragonite
(These two are desperate)
Confusion/Shadow Ball Alakazam
Confusion/Seed Bomb Exeggutor

DPS order vs. machamp

I've soloed two of them. Used Espeon (did a lot of damage, but doesn't last very long) and then used a Blissey with a psychic quick attack and Hyperbeam.