Calix does not have summoning sickness and cannot be blocked by an opponent.
Steps
Deal combat damage to an opponent using Calix.
Calix's second ability triggers, creating two token copies of Three Blind Mice.
The Three Blind Mice tokens enter the battlefield with two lore counters on them due to Doubling Season, triggering their first and second chapter abilities, as well as Calix's first ability twice.
Resolve both Calix triggers, putting two +1/+1 counters on a creature you control.
Resolve the first Three Blind Mice triggers, creating four 1/1 Mouse creature tokens.
Resolve the next Three Blind Mice trigger, creating two token copies of a Three Blind Mice token.
Repeat from step 3.
Once you have infinite Three Blind Mice triggers, you may use them to copy any token(s) you control.