Search within "text" field in discover mode

kibana filters in "discover" mode seem to have "exist", "is", "is not" but no "contains" value.

Is there any way to use "contains" for a text field?
e.g. with Elasticsearch Query DSL?

Yes you can click on "Edit as Query DSL", then you can rewrite the query like this:

Oh and even better the "is" operator is misleading because behind the scenes it's a "match_phrases" query:

In your example "customer_first_name" already exists as a tag.
But in my case there is a large tag called text and I want to search within this field.

In your case it would be something like
"customer_first_name_contains": "mina"

When I try to make such queries I get an error....

could you share your query and the error you're getting? thx!