If you don't want to deal with the used market (which might be necessary to get super cheap) the Intel Arc a310 cards have HDMI/Display Port and are slot powered so no PCIe power needed. They're also sought after for their quite good video transcoding performance so reselling it after you're done would be pretty easy.

Get a used SFF office PC low profile card off Ebay. They often have chipset wattages around 25 or so and easily run on slot power only

Something like this: https://www.ebay.com/p/1958445856 (idea only, not endorsing this seller).

Anything of a semi modern format with a pcie interface thata not an outright scam card will be fine for VGA no-driver video output. IME older AMD/ATI cards seem to boot better than oder NVidia cards...

The nVidia GT series are cheap, the 710 series are the cheapest new cards that I have found.

Alot of servers have at least one built in video output head but if it's an older device you might need to look for an HD15 VGA port... Some servers might have had some sort of micro port or proprietary port/dongle setup as well. Might refer to the documentation for the chassis/motherboard first... It's possible you have what you need already.

eBay, Craigslist, Goodwill, Facebook marketplace, or whatever your local equivalent is. Most basic graphics cards don't need additional power.

There exist USB graphics adapters, too. But they can be janky and may not show the boot process.

Check your local Craigslist or other classifieds for cheap old GPUs. Or if you have another PC, borrow the GPU and power supply just to get it to boot.

If the motherboard has any available pcie slots (and the chassis has space for it), minimal graphics cards with HDMI or VGA or whatever else can be had for really cheap. That's what I use to troubleshoot my truenas box.