Right this moment, probably not. A little over a month ago I started looking to build an inexpensive office computer with a hard $400 budget.
Here are some of the parts ideas I came up with, but even then it was always just a few $ above my limit. Unfortunately, since then, the price on most of these components has gone up, or the part isn't available.
My list consisted of the following parts, and some of them general. The PSU is CRAP.
I was working along the lines of:
i3 10100 and using it's stock fan - it was $99
The absolutely cheapest B4xx motherboard I could find. I was trying to locate one with 4 RAM slots for future needs ~$75
At the time the Ballistix RAM kit was the cheapest I could find for 16GB. also ~$75
Samsung 250GB 2.5" SSD- $40
The topping on this cake of cheapness was a Rosewill case with an included "400W" power supply. Total junk and dangerous, BUT given the system should not pull more than ~130W on load, it seemed a worthwhile risk for this use case. -$50
SO, we come to ~$340 or so (at that time) with no OS. This was also based in shopping at a local MicroCenter.
You will find that most of these prices have gone up in the area of 10-20% in the last couple of weeks and a good portion of it is unavailable via Amazon and the like.
Your use case would CRUSH the poor thing.
I honestly think your only option at that price point is to search used without a video card, and or office refurbs which are also priced out of the market.
GL