 by the action of the agent. its being preceded by nonexistence is not by the action of the agent so it has no connection to it. the condition of it being an action is the condition of something that the agent has no influence on in any way. as for your saying that the existent cannot be brought into existence if you mean by that that it cannot resume existence after nonexistence then that is correct.
بفعل الفاعل. فكونه مسبوق العدم ليس بفعل الفاعل فلا تعلق له به. فاشتراطه في كونه فعلا اشتراط ما لا تأثير للفاعل فيه بحال. وأما قولكم إن الموجود لا يمكن إيجاده، إن عنيتم به أنه لا يستأنف له وجود بعد عدم فصحيح.