Very difficult given the relative power at the time. Siberia was populated by more primitive peoples with a lower population and immature state building. Persia had the population, resources, and sophistication to fight the Russians much more effectively.
Russia couldn't even reach the Black Sea until the 18th century because of Muslim opposition.
Russia could and did reach the Black Sea from the late 16th c. and repeatedly dislodged the Ottomans.
What they couldn't do was 1. solve the incredible logistical puzzle of getting a large army into Crimea without a navy 2. hold on to what they got because of the nature of armed service (gentry militia and streltsi had limited conscription times and had to go home at the end of fighting season, cossacks were reliable only until next election of colonels/hetmans, the Kalmycks had limited numbers).
Persia is ridiculously overambitious, btw. The Russians managed to lose a whole 17th c. army to logistics and local politics in Daghestan, and then another one in Turkmenistan already in the Petrine era. I mean the Volga was still almost frontier land though most of the 17th c. too.
Considering how good Russo-Persian relations were in the 17th and 16th c. (and most of 18th too), it would be sort of really illogical for the Russian state to take upon the goal of fighting a fairly good neighbour/customer/sometime ally when there is Poland/Ottomans/Sweden to worry about. The Persians, unlike the Tatars/Turks, aren't raiding you every year for slaves, and there isn't a Holy League formed against the Persians. They buy Russian manufactured goods and sell luxury items. Why fight them?