Actually the chicken and egg situation has been avoided by the statute. You have 30 days after making the recording to serve notice of a compulsory license, but you must have the license before distributing it to the public.
"17 USC 115
(b)
Notice of intention to obtain compulsory license.
(1)
Any person who wishes to obtain a compulsory license under this section shall, before or within thirty days after making, and before distributing any phonorecords of the work, serve notice of intention to do so on the copyright owner. If the registration or other public records of the Copyright Office do not identify the copyright owner and include an address at which notice can be served, it shall be sufficient to file the notice of intention in the Copyright Office. The notice shall comply, in form, content, and manner of service, with requirements that the Register of Copyrights shall prescribe by regulation."
(2)
Failure to serve or file the notice required by clause (1) forecloses the possibility of a compulsory license and, in the absence of a negotiated license, renders the making and distribution of phonorecords actionable as acts of infringement under section 501 [17 USC 501] and fully subject to the remedies provided by sections 502 through 506 and 509 [17 USC § §502-506 and 509]."