Yes, you can progress to a new tier either by collecting enough Tier Miles, or by taking enough qualifying flights.
The thresholds for each tier are as follows:
Silver: 25,000 Tier Miles or 25 qualifying flights
Gold: 50,000 Tier Miles or 50 qualifying flights
Platinum: 150,000 Tier Miles and at least one qualifying flight* in First Class or Business Class
*Effective 1 April 2023