So it looks like the best route is TB2, so basically an nvme adapter with a DisplayPort connector?
There are not too many TB1/2 options for NVMe SSDs, but there are some.
The downside is that they are expensive, and questionable speeds.
But, any NVMe solution that will get better than the internal SATA SSD speeds will be expensive. Not sure what you are trying to do with your 2012 Mac Mini, but it might be more cost effective to buy a newer Mac.
Someone talks about tb3 nvme drive on Tb2 to Tb3 adapters, however not sure how fast all the gig will be....
I have booted from TB3 NVMe SSD using Apple's bidirectional adapter. I used the NVMe on multiple Macs, but I only did speed tests on a Late 2012 iMac. I was able to get up to 900MBps over the TB1 port.
To use a TB3 NVMe over the bidirectional adapter on older TB1 and TB2 Macs, the NVMe drive needs to have its own power source or be powered from another TB3 device, such as a TB3 dock.
It works and is probably the fastest single drive you can get for your 2012 iMac, but it isn't cost effective.
You can probably find a TB3 dock that has its own power source on eBay for around $100, maybe cheaper.
Apple's bidirectional adapter costs $49 new, but can sometimes be found for a little cheaper on eBay. Only Apple makes this adapter, I wouldn't try any other adapter claiming otherwise.
You will also need a TB1/2 two cable to go in-between the Mac and the bidirectional adapter, maybe $30.
Then, you can start shopping for TB3 NVMe SSD, depending on the size, could easily be $400.
So, not cost effective. If you already have some of the above, then maybe not too much out of pocket costs, but for most, they would rather just buy a cheap M1 Mac Mini.
Other possible solutions:
While I have never done it, you can get faster USB speeds from TB3 docks. You can use a fast 10Gbps USB NVMe drive, which will be a lot cheaper than a TB3 NVMe.
There are some TB3 NVMe enclosures that have their own power. I forget where, but I saw one that had four NVMe slots, but I think it was meant to be used with HW RAID, and the individual slots were slower than TB3 speeds.
There are external PCIe expansion card enclosures for both TB1/2 and TB3 that could be used with a PCIe NVMe adapter, but the enclosures are expensive.
RAID0, either with an external HW RAID enclosure or using two internal SSD over SATA and a SW RAID0. This would get you about the same as an external TB3 NVM on your TB1 port, just for a lot cheaper. I ran boot drives over SW RAID0 for years on my Mac Pro.
