TL;DR: Between the development of the Beluga and the Dreamlifter, the An-124 took over the commercial large cargo market. Therefore, Boeing didn't have a business case for charters.
As mentioned in vasin1987's answer, the A300-600ST Beluga is certified for commercial operations whereas the 747LCF is not. Airbus originally intended the aircraft to be available for charter, so they went through all the certification work, whereas Boeing did not.
The reason why has to do with the time periods in which both were built. The Beluga project began in the early 1990's. Consider the very large haul capability at the time: the US military-only C-5, the aging Guppy, and the An-124.
The An-124 would be well suited, except at that time, it had no civil certification and Ukraine and Russia were still getting over from the collapse of the Soviet Union. Prior to that, it would be politically difficult in many places to do business with Aeroflot, the Soviet Union's air carrier.
By the 2000's, Antonov and Russian operators realized there was a heavy lift market, and their aircraft was very well suited for it. Airbus was successful, and with increasing production rates so the Belugas were needed for internal use. The An-124 took over the charter market.
It was under this context that the 747LCF project started. Both the Beluga and the Dreamlifter have high cargo floors that require special equipment or crane for loading, a severe disadvantage against the An-124. So Boeing didn't have a business case to pursue charters.
Things have changed once again, with the political situation between Ukraine and Russia, the An-124 may not have support, so keep an eye out for what will happen.