Absolutely not!

I joined last week for free, and by completing enough matches for "Blessing of the Gods" I earned GODS. There are a few convoluted steps for using them, but they represent the first minted value you can begin acquiring.

If you have a knack for the MTG/Hearthstone playstyle, you can do well enough that you'll earn minted cards on the weekends through the Weekend Ranked event and continue improving your deck during the week with core packs and the Star Store.

Basic goal:

1. Play games for XP (earn core packs every level)
2. Earn Star points for wins (buy locked/minted core cards)
3. Earn Flux for "Running the Gauntlet" (up to 3 wins per God per day)
4. Earn GODS for winning 7/14/21 games with X games played against Y unique players
5. Win N out of 25 games on Weekend Ranked events (11+ wins includes minted card packs)
6. Forge locked core cards into minted (Meteorite quality) cards that have value

By having locked core cards off the blockchain, you can play the game comfortably without feeling the need to buy to enjoy the game. The play2EARN part kicks in when you have dupes of cards that you merge in the Forge.

Check out the community for lots of tutorials for F2P players just starting out :)