Nope, you have to make some sort of purchase. From Steam's help pages:
"No Purchase Older Than 7 Days
Your account must have a successful purchase older than 7 days, but not older than a year in order to access the Community Market. The purchase of wallet funds, games, DLCs and software meet this requirement. Activating a Steam Wallet Code or Gift Card on your account to add funds to your Steam Wallet also meet this requirement. Retail CD key activation and gift purchases do not satisfy this requirement.
Any purchase that is charged back on your account will reset this restriction. Only purchases after the most recent chargeback will be considered for purposes of this restriction."