Once again, we must look at the context. Note that in v. 16 Paul points out that Christ created all things. So then in translating v. 15 we cannot say that He created Himself. The genitive is thus a "genitive of subordination," and may be translated "over." The Greek genitive is often translated something other than as a possessive.
Vincent's Word Studies has: "We must carefully avoid any suggestion that Christ was the first of created things, which is contradicted by the following words: in Him were all things created. The true sense is, born before the creation. Compare before all things, Col_1:17. This fact of priority implies sovereignty. He is exalted above all thrones, etc., and all things are unto (εἰς) Him, as they are elsewhere declared to be unto God. Compare Psa_89:27; Heb_1:2."