Well. Kind of. At the height of the Swedish Empire (around the mid 17th century) there was no city called St. Petersburg. The city itself was founded in 1703 when the Swedish Empire had started to face some very serious problems already.

The Russians had captured the fortresses of Nöteborg and Nyen in 1703 and built the fortress of Kronstadt on an island outside the mouth of the river Neva. In 1704 and 1705 Sweden made repeated attempts to take Kronstadt (effectively opening the route to St. Petersburg itself) with naval landings but despite repeated efforts the fortress remained firmly in Russian hands.

In 1708 the Swedish army of Finland invaded Ingria and crossed the Neva river but was surrounded and had to be evacuated by ship (and forced to slaughter 5000 horses as it retreated, a huge loss).

You have to keep in mind that for the first 3 years (1703-1706) the main Swedish army was marching back and forth in Poland, Saxony and Lithuania trying to end the war there. By the time it was ready to move north in 1707 Peter offered to return all lands gained except St. Petersburg to Sweden.

The Swedish army suffered badly in the winter of 1708/1709 and was finally defeated at Poltava in 1709, a defeat it would and could never recover from.