Tvesa, who missed an Olympic berth, had three birdies between 14th and 17th to register a score of three-under 68 on an opening day at the Aura Golf. She is lying two shots behind leader Ursula Wikstrom (66) of Finland.
Among other Indians, Diksha Dagar, part of the winning team at Aramco Ladies Open in London last week, was T-18 with 72, while Vani Kapoor (77) was T-74 and Astha Madan (79) was T-95th.
Tvesa, 25, visiting Finland for the first time, got off to a pleasing start. ''The greens are rolling really pure, so I was excited to play on such great greens. It is my first time here in Finland and I am enjoying it,'' she said. ''The weather is very similar to back home, so I'm feeling quite at home with that. I had four birdies today, I made some good putts coming in in the last few holes. The greens are rolling quite well, and it was important to make a few of them.
''I would like to get better than my career-best of T-6 at the 2019 Hero Indian Open and Jabra Ladies Open this year. So there is a lot of incentive to do that,'' she added. Wikstrom, who was out in the first group of the day, started on the 10th tee and carded a round of five-under-par, which included seven birdies and two bogeys.
Argentina's Magdalena Simmermacher and Tvesa, both sit two strokes behind the leader on three-under-par.
Four players are tied for fourth place on two-under-par, including the 2021 Race to Costa del Sol leader Atthaya Thitikul, Spain's Noemi Jimenez Martin and Harang Lee, and Austria's Christine Wolf.
Finland's Leena Makkonen sits in solo eighth place on one-under-par, while there are nine players level par for the tournament, including five Finns.