Free games don't drop cards until you spend money on micro-transactions or dlcs, they are the most expensive way to get cards. Cheapest way to get cards is to search the store for '[/] games' with '[/] cards as a feature' and then sort by price.

Or buy cards from 3rd party key resellers, but expect some purchases to go bad.

https://psteamproxy.yuanyoumao.com/search/?sort_by=Price_ASC&maxprice=4&category1=998&category2=29&specials=1