Does Suspend count as casting a spell for effects that care about casting from hand?

Suspend has two distinct steps. First, you exile the card from your hand with time counters on it — this is not casting a spell (CR 702.61a). No spell is put on the stack at this point, so effects that trigger or care about casting a spell from your hand do not see this action.

Second, when the last time counter is removed, you cast the spell without paying its mana cost (CR 702.61d). At this moment a spell is cast, but it is cast from the exile zone, not from your hand. Effects that specifically require casting from hand — such as Leyline of Anticipation's predecessor cards or prowess triggers worded "whenever you cast a spell from your hand" — will not trigger.

Standard cast-from-anywhere triggers (e.g., a simple "whenever you cast a spell") do trigger at that second step, because a spell is genuinely cast. Only the zone restriction separates these cases (CR 601.2a, which specifies that casting begins by moving the card from a zone to the stack).

Concrete example: You suspend Ancestral Vision (0 mana cost, 4 time counters). On the turn the last counter is removed, you cast it from exile. A Monastery Mentor that reads "whenever you cast a noncreature spell" triggers normally. However, an effect reading "whenever you cast a spell from your hand" does not trigger, because Ancestral Vision came from exile, not your hand.

In summary: suspending ≠ casting (CR 702.61a); the later cast is from exile, not hand (CR 702.61d); only generic "cast a spell" triggers apply at that point.