How to do third-party view tracking without cookies?

Given a third-party webpage www.somepage.com handing out specific URLs to subscribed websites in the format of www.somepage.com/site/3ir3jsd - how can I track that a user having an account on www.somepage.com has visited one of the subscribed websites without resorting to cookies / localStorage ?

A standard approach would be to store a cookie for www.somepage.com and add www.somepage.com/site/3ir3jsd via an IFrame. This has several issues as new laws and browser defaults prohibit third-party cookies and local storage to be loaded.

Is there some other mean to achieve this? I see that this is a potential privacy issue and would of course ask for permission to do this and would prefer secure / non-privacy-infringing methods. All major browsers have to be supported which rules out browser extensions too (looking at you Internet Explorer 9-11). Maybe JavaScript? But I don't want the user to have to "login" to my pages service on every subscribed webpage. Storing their session cookie in the first-parties localStorage / cookie is a potential security risk though (which would be needed when using JavaScript + storing their session data).

Another approach I have checked is client certificates but they are poorly supported (read: often unsupported) by mobile browsers and the use-ability of adding them is horribly in most of them too.