Can you cast a card exiled by suspend before its time counters run out?

Suspend (CR 702.62) works like this: when you exile a card with suspend, it gets a set number of time counters placed on it. At the beginning of each of your upkeeps, you remove one time counter from it. Only when the last time counter is removed this way do you get to cast the spell — and you must cast it at that point if able (CR 702.62d).

There is no rule that allows you to voluntarily cast a suspended card while it still has time counters on it. The card is in exile, a zone from which you generally cannot cast spells unless a specific effect grants you that ability (CR 702.62b). Suspend itself only grants casting permission at the specific moment the last counter is removed.

However, you can accelerate the process indirectly. Effects that remove counters from permanents or exiled cards (such as proliferate working in reverse via cards that remove counters, or spells like Clockspinning) can remove time counters faster. Once the last counter is gone via any means, the suspend trigger fires and you cast the spell for free.

Concrete example: You suspend Ancestral Vision (suspend 4). Each upkeep a counter is removed. On the upkeep when the 4th counter is removed, you must cast Ancestral Vision for free. You cannot choose to cast it on upkeep 2 or 3 just because you want to draw cards sooner — you must wait for that final counter to come off.

Relevant rules: CR 702.62b (card goes to exile with counters), CR 702.62d (cast when last counter removed), CR 601.3 (casting from unusual zones requires explicit permission).