With this picture, and there no pedals showing, then I think you’re doing a motor bike without pedals?
I have with my new build which is without pedals and meant for the dirt, made my own clamp to spokes with pulley and v-belt. Then jack shaft and gear, chain, and clutch.
I have not ever used the gear that is part of the original part on the rear wheel. The gear is small and that makes for too high a gear. Possibly someone out there knows if it can be used along with other gearing down on a jack shaft to compensate?
The offset that would be required with the engine shaft on opposite side to utilize that existing gear would not make sense to me, too much off balance.
I made a motor bike with engine offset, but I had the pulley on the rear wheel as the same side as the engine shaft. Once I got going it was not too bad, but the engine had one side interfere with the foot peg and comfort.
The jack shaft with gear & bearings can be purchased for around $25.00 and I got one and used both welding and bolts to set it up.
(oops a little low I remembered .... AZ1826-12 Jackshaft kit 5/8 by 12 from Azusa Engineering Incorporated from a go cart shop nearby for only $32.95.)
(See post below with more info from me Measure Twice)
******** note I just got to getting quite a bit more done on my build now, and I am going to probably remove 2 or 3 inches of the jack shaft since it is too long, but better to have too much than too little
I have not yet tried my newest build, but it is with 26inch tire and a total effective gear reduction of 8.3 to 1. I've never used a clutch before on motor bikes I built, as before I just pushed and it started and vice versa. Pretty much the same size gearing parts, but the wheel at 24 inch dia, so it was slightly greater gear reduction.
If I find the clutch is not what I want for any reason, I replace it with a gear and do the same as my old push start. Holding the rear wheel off the ground and using a starter cord was not as easy.
Hope that helps.
Measure Twice