As mentioned I think free version of resole is CPU oriented. In studio version, Encoder: Auto (should I select Native). Nvidia option is what I always use, but I'm not sure if its even there in free version of resolve. You can try third party codecs and see if that will work on your version.
I personally like using: MainConcept Codec Plugin for DaVinci Resolve Studio. Its not cheap but has some great results.
https://www.mainconcept.com/blackmagic-plugins...but its for studio I think, also not free version. Also available is Voukoder, but again I'm not sure if it works on free version.
Voukoder is a system wide video- and audio encoding service for Windows that improves your media encoding experience. It supports various modern encoders and also provides a set of post processing filters.
Currently supported are:
• BlackMagic DaVinci Resolve Studio
• Adobe Premiere Pro
• Adobe Media Encoder
• Adobe After Effects
• Magix VEGAS Pro
• and more ...
If present Voukoder can make use of hardware acceleration (i.e. Intel QSV, NVidia NVENC or AMD AMF) to speed up media encoding even more.
https://www.voukoder.org/Also I think I saw a release note for Fusion 19:
• Up to 2x faster H.264 and H.265 native encodes in Windows.
...you can try that. Also you can try using workaround I use even with studio version if you are working in fusion page. Which is using saver node to save image sequence and than re-import that with a loader and encode that. Usually works faster, especially with Fusion effects which many of are still CPU powered.
I haven't tried it, but you can maybe export image sequence from resolve free version and re-import that for encoding with cpu, which should be faster. Replicating what I do from fusion.