Can I do a forward secure half-round ephemeral-static ECDH?
I am curious if we can possibly ensure the forward secrecy under this scenario with only one round of communication.


I do not believe so; the protocol can be summarized as:


Alice publishes her long term key
Bob does some work (without having Alice do anything)
Alice does some work, and retrieves the message


If, anywhere between points 1 and 2, Alice's state was copied, then the copy of Alice's state would be able to perform step 3 just as well as Alice did, and so you don't get PFS.

Also, terminology correction: you asked whether this can be done with only one round of communication; actually, it can, by having Alice send a message at the start of step 2.  Obviously, this doesn't work for your project; what you need is actually a 'half round' exchange.