Word for consciously doing something without knowing that it is already a thing

Solution 1:

I thought of unknowingly when I read your post.

From The Free Dictionary:

unknowingly - without knowledge or intention; "he unwittingly deleted the references"

Synonyms: inadvertently, unwittingly

Solution 2:

Also consider unconsciously. From en.wiktionary, it means “In a subconscious manner; something done unknowingly”.

Note that subconscious has multiple senses, ie both “below the level of consciousness” and “partially conscious”, neither of which is right for the question's situation. The latter part of unconsciously's definition, “something done unknowingly”, certainly applies.

Also consider the collocation all unawares, meaning completely unaware. In addition, a case might be made for using the term supra-consciously. From en.wiktionary, supra- means “above, over, on top” or “greater than, transcending”. People who offer hints of hotter or colder know quite well what they are doing, but are above looking about for a name for the activity.

Solution 3:

The first word that came to mind for me was intuitively.

See intuition at dictionary.com:

direct perception of truth, fact, etc., independent of any reasoning process; immediate apprehension.

This would cover the aspect of knowing how to play the game without ever really thinking about it. As mentioned previously, unknowingly covers the aspect of doing it without realising.