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The artillery company seems to have been formed between 1773 and 1780.
According to Город над Авачинской бухтой by Витер, Magnus Carl von Böhm, chief of Kamchatka from 1773 to 1779, sent 32 soldiers with two officers to Petropavlovsk. These built an artillery battery at the entrance to the harbor.
According to Clerke in Kamchatka, 1779: New Information for an Anniversary Note by Crownheart-Vaughan, officials from Catherine the Great on down got very interested in reinforcing Petropavlovsk after the English visits. The governor (I think governor-general) at Irkutsk sent "four cannoneers, [and] three noncommissioned officers" along with new commandant Reineke, who according to de Lesseps, was installed in 1780.