Currently the logic that governs whether or not a user can see/access a CTA link for a quiz differs between what is shown on the timeline block and on the module's view page.

For the timeline block, the CTA link is governed by the criteria in  mod_quiz_core_calendar_provide_event_action which only checks whether it has the capability, the quiz's time restrictions and whether or not an attempt exists.

This differs from the additional restrictions checked in the module's view.php page which e.g. also checks unfinished attempts, total number of attempts.