It looks like a 20" wheel so the stays are incredibly short compared to a 26" MTB or a 700c road bike. I have a very similar-looking folder that started as a 1x6 with 14-28 tooth freewheel, and group parts topped out at tourney level.
To improve the ratios I put on a triple front crank which was rescued from a donor MTB. I built an 8 speed freehub into the original rim, and fitted an 11-32 tooth 8 speed cassette, and upgraded to deore V brakes/levers. I had to cut the freewheel with a grinder to get it off, cos they hadn't used a standard fitting or any grease.
Since the frame doesn't allow for a front derailleur, I shift at the front by hand. As a consequence, the bike can drop the chain pretty easily.
FIRST - before you get stuck in, try modifying your pedal stroke. Try pedalling in circles and keeping an even tension on the chain not riding like an 8 year old all choppy. This will help by keeping the incremental change per tooth smaller as it spins the chain onto the teeth.
SECOND I suggest that you start by cleaning the chain and cogs and chainring. Check the chain for wear, and eyeball the chainring for wear (should be fine given the limited mileage).
You should also eyeball the chainline - look down from above and the chainring should be in line with about the middle of the cogs. It could be biased a little to the outside, but should not be outside the lines of the cogs.
Also, ensure your chainring is flat too - if the chain always drops at one point on the rotation then it could have "a divergence from the plane" Without the chain on the teeth you should be able to spin the cranks and see the teeth all in line from above, with no/minimal wobbling side to side. Small areas of deflection could throw the chain.
THIRD put the chain on the biggest cog, and look at the bottom chain run - it should be pretty forward. This is testing whether you can remove one or more links to help add tension to the chain in the smaller cogs.
FOURTH take that broken chainguard off and try to fix it. It should not have a glaring gap as per your photo so maybe the chain coming off has broken it. The chainguard does help somewhat keeping the chain on the chainring, but its more for reducing the trouser-cuff contact with the oily chain. Given this bike is a 1x you could fit a chainguard ring that stands a little taller on the outside.