Yes, you can create your own GIFs and upload them to Wave.video. Here's a helpful article on how you can create your own GIFs.
Once your GIF is ready, you can upload it to Wave.video. To do it, head over to the step "Graphics & Stickers" and click the button "Upload".
You can also upload your GIF on the step "Add Videos & Photos". Switch to the tab "Uploads" and upload your GIF here. You can then add it to your video on the step "Graphics & Stickers".