In my opinion, "at" is required here. There are circumstances in which we simply use "any time" but I don't think it works here. "At any time" is the same as "at any moment" in your context and "at" can't be omitted in that phrase.
Please note that I have changed your thread title. Titles should include some or all of the words you are querying. Non-specific titles like "Is this correct" or "Help please" are not helpful when we are searching for threads, and it helps you to tell your own posts apart.
Also, please check the information in your profile, particularly the "Current Location" - it appears to be incorrect.
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