no. that would be something like "we likes" or "we am"
"lubimy" is a form of "lubić" =to like , that goes with "my", no other form can be used with "my" (in present tense).
But because "lubimy" already contains information about "my", it is unnecessary, and is usually omitted, unless you want to make a point that it's us who likes cookies.
(ja) lubię= I like
(ty) lubisz= you like (1 person)
on/ona/ono lubi = he/she/it likes
(my) lubimy= we like
(wy) lubicie= you like (2+ people)
on/one lubią = they like
The sentence "My lubie ciasteczka" is not correct, but your sense of redundancy in proposed exercise is very correct and valuable. In fact,
Polish speakers rarely use personal pronouns, because the conjugated
verb has all the necessary information. In contrast, English conjugation (reduced to almost "no conjugation") requires and "glues" the personal pronoun to the verb, because without it the verb has very little meaning:
Conjugation of the verb:
lubić - to LIKE
Lubię ciastka - I LIKE cookies
Lubisz ciastka - You LIKE cookies
Lubi ciastka - He/She/It LIKES cookies
Lubimy ciastka - We LIKE cookies
Lubicie ciastka - You LIKE cookies
Lubią ciastka - They LIKE cookies