How do I know I have enough clay in my soil to make a cob oven?

And if I don't, is it still possible to make one?

Use test bricks or the sedimentation test to assess your soil: http://www.weblife.org/cob/cob_043.html

You can increase clay content by adding lots of water and then removing settled sand and silt (clay remains suspended in the water).

Quarries sometimes have clay they need to get rid of.