Short answer: No, there is not a rule for which 3rd person ending a noun will take if it ends in a consonant. You have to memorize it as part of learning the noun.
There's a little more discussion here: https://www.duolingo.com/comment/18281289
I think after a while though you will develop a sense for it, and if you get it wrong, it doesn't make a big difference in practice. It's something that even native speakers occasionally have to look up or ask about.
A good dictionary will show the 3rd person possessive form.
The only one that I know online that provides this is Wiktionary.
For example, kert takes -je
While világ takes -a
You can also look into dict.cc. Might be a bit easier to handle. Right above the entries on the left side, it lists the noun's base form, accusative, plural, and 3rd-person singular possessive form.
Wiktionary is a lot more comprehensive, though, if you want to look up special forms.