Jake Paul and Jutta Leerdam made their first public appearance as an engaged couple on Wednesday ... and they put the Olympic speed skater's massive new accessory on full display.

The lovebirds hit the premiere for their new Max Original show, "Paul American," just now ... electing for all-black outfits after rocking white ensembles for the proposal in Saint Lucia.

Jake and Jutta also did some prom-esque poses ... proving they don't mind getting all mushy for the cameras (something they're used to at this point).

TMZ Sports spoke with the Paul Bros about the big show ... and they admitted it took some convincing to get their partners on board, but they ultimately agreed to be involved -- and they're thrilled to show the world how special they are.

The big event was held at Tempo by Hilton New York Times Square ... and of course, the whole family was there to celebrate the release.

Greg Paul showed up with Hawkwind Kelly as Pam Stepnick arrived solo ... and Logan rolled through with his fiancée, Nina Agdal.

The show will be available for all to stream on Thursday ... and if we know anything about the Pauls, it's gonna be quite eventful.