It's an adverb.
Already is not a verb so does not have a past participle form.
"Had" is already the past participle of "have".
Cooked is already the past participle of cook. The present participle is cooking.
Known is already the past participle of know.
Jumped is already the past participle of jump.
Tried is already in past participle form. It is the past participle of try.
Burning already is the present participle of burn.
Thought is already the past participle of "think".
Consumed is already in past participle form. It is the past participle of consume.
"broken" already is the past participle of "break".
Bringing is the present participle of bring; brought is already in past participle form.
Imagined is the past participle of imagine.