I would rush a triforce, and I wouldnt recommend backing until you have enough gold for at least the phage. His passive gives you crazy attack speed, so focus building damage and health early game - items like BotRK and Tri will give you loads of attack speed anyway. I usually find that E>Q>E>W is a strong combo, as it gives you the stun and a chance to chunk a good portion of their health.
Keep in mind his W is a great escape tool as you can jump to minions or wards or champs. If you ever find yourself in the middle of a fight and you're getting low, pop that E! You can get the stun off and secure a kill or get the hell out of there if you need to. Other than that, if you can cs well (and Jax is probably one of the easiest champs to get cs with in the game) than I think you should have a viable chance.
If you're still having trouble early game, mabye try and spam health pots? I've found out that having a ton of those on hand gives quite a bit of sustain when I play squishy early game champs like Jax, Kata, Akali, etc.
Hope it helped!