They have me working nights from 3pm to midnight as my regular shift, as the only person at lvl1 support. The company has over 200 clients averaging 75 users each.
What's the average call volume during that time frame? What kind of response times are they expecting? Having a lot of customers doesn't mean too much if most of them close two hours into your shift.
Though I am wondering, is it normal for an MSP to expect someone to do this work effectively with a total of 10 days of training?
Probably depends on their assessment of your experience and skills. It wouldn't be a call I'd make, but I'm a big fan of teamwork and making sure everyone feels they've got adequate support to get their jobs done.
Granted, the last MSP I worked for hired me on primarily to do development and deploy a few new tools they wanted. It was a pretty bad day if I was working a customer call.
They just kind of threw me into the woods and told me to fend for myself or else.
Yeah, that's a pretty shitty thing to do.
This is my first job and the night shift I am realizing is burning me out since I feel like I am on my own.
Surely it can't be that busy at 10pm? If it isn't, use that as time to expand your skills to get more comfortable. If it is very busy, take that on up the chain and back it up with data. Their response will be telling. A good MSP will change their scheduling to address the problem (because it would be very unprofessional to offer SLAs without actually staffing the desk well enough to handle them).
There are oncall personnel but most of the time I can't get a hold of them when I am stuck.
This is probably something to bring up as well. Point out that you all can't meet SLAs if the one guy on the desk can't solve the problem and can't get support from the next tier up.