Putting a variable in a query in URL param with an object?

I am sorry that I have confused things.

What exactly should be sent on the URL?
https://foo.com?filter[q][metadata_jcont]={"first_name":"David"}

Any link to your API would help.

Also messing around I was able to get filter[q][metadata_jcont]={"first_name":{{firstName}} } to not throw an error - notice the space between the last '}} }'