I think I recall seeing the Swedish version of this word listed among cognates with "boy". It seems probable from the pronunciation that the Swedish word is loaned from Finnish, and not the other way around. The meaning is identical to "boy" and the pronunciation is close.

I don't remember seeing any source confirming or refuting the connection.

This is the entry for 'poika' in a Finnish etymological dictionary (Nykysuomen etymologinen sanakirja), run through deepl:

"The word has definite etymological equivalents in both closely related and distantly related languages, e.g. Karelian and Votic poika, Ludic and Vepsian poig}, Estonian poeg, Livonian puoga, Komi and Udmurt pi, Mansi pig, and Hungarian fiu. Possible equivalents are also the initial parts of the Mordvin word pijo 'grandchild' and the Mari word puerge 'male person' (erge 'man'). The original form of the word has been reconstructed as *pojka. The Swedish pojke, which in the past also meant 'servant boy', is apparently a loanword from Finnish. In contrast, the English boy and the etymologically related German Bube have different origins."

From what I can see, the etymology for "boy" beyond relatively modern cognates is still undetermined. It could have entered germanic before 900 and left no written traces before later appearing in Middle English. Finns and Estonians were involved in sea trade around that time (borrowing words such as kauppa, cognate with "shop") so a word for "servant boy" would have been useful.

In particular, the pronunciation of Estonian "poeg" and "poiss" seem too close to be entirely coincidental.