Perhaps the quickest way would be to reuse existing technology, especially one that already has an established user base. In particular, it should be possible to extend some Fediverse (ActivityPub) clients and servers to add a new type of message that represents introducing yourself to a prospective date.
ActivityPub is built on ActivityStreams[0], which already has a way of representing relationships[1] so it could be extended with the relation "Would Like To Know"[2].
You could take something like Mastodon and add a property to the profile data[3] so that users can state whether they are willing to receive such introductions from other users. (Users should perhaps also be able to specify a maximum number of such introductions that a user attempting to contact them can send per month, to stop people from sending out introductions to everyone that's available).
Unfortunately there isn't currently a universal search feature in Mastodon[4], but it might be possible to add that as a hack by caching all opted-in profiles on each instance.
[0] https://www.w3.org/wiki/Activity_Streams_extensions
[1] https://www.w3.org/TR/activitystreams-vocabulary/#connection...
[2] https://vocab.org/relationship/#wouldLikeToKnow
[3] https://docs.joinmastodon.org/spec/activitypub/#profile
[4] https://github.com/tootsuite/mastodon/issues/9529