Zoom to desired area. Click "Extent" on upper left, and draw box outlining relevant area
Tick "Elevation Products (3DEP)" on left menu
Select "1/3 arc-second DEM" and click "Search Products" (Blue button)
Click "Download Link (TIF). Or, add necessary files to cart, view cart, and download GeoTIFF files
Trim Data
Download and install QGIS or use package manager. Launch it.
Click "Data Source Manager" (upper left, three little squares icon)
Choose "Raster", and choose source file downloaded. Click Add, then Close.
The downloaded data will be larger than the area you selected, so if it's hard to find the feature you chose originally, you can add an OSM layer by following the steps above but going to XYZ, then OpenStreetMap.
In QGIS menus, choose Raster -> Extraction -> Clip Raster By Extent -> Choose dialog for "clipping extent..." -> Select Extent on Canvas -> Choose desired area
Choose "Clipped (extent)" chooser menu and name output layer.
Convert to STL
Install "DEMto3D" plugin (plugins -> manage and install plugins)
Select Raster -> DEMto3D -> DEM 3D Printing
You can choose "select full extent" to do the entire thing.
0.2mm spacing works well for smaller models, 0.1 for more detail. Check your physical machine's capabilities.
Enter width and length.
For height field, a positive value will "chop" that many meters off the original model. If you set it to the minimum elevation in your area, there will be no extra base padding.