Timofeeva came through three rounds of qualifying and got past experienced Frenchwoman Alize Cornet and 2018 champion Caroline Wozniacki in her opening two rounds before pulling off a 7-6(7), 6-3 upset against 10th seed Haddad Maia.
"I'm still curious how far it will go. Just now I know what I'm capable of, that I can compete with these girls," Timofeeva told reporters as she prepares to face Ukraine's Marta Kostyuk.
"And I was just curious to see if it's possible or not, like should we work on something? Of course there's something to work on. That's always (there).
"Now I'm just a bit more confident in my powers and we will see what it will bring us."
Timofeeva is playing some of her best tennis at the year's first Grand Slam but faces a tricky test against Kostyuk in the fourth round after the Ukrainian beat Russian Elina Avanesyan in a contest that had geopolitical undertones.
Timofeeva may not get a handshake from Kostyuk following their match but is keen to finally face her.
"Marta's just a year older than me," Timofeeva said.
"But we didn't cross paths in juniors because she started to play well in the professional tour much faster. She was already I think rocking the WTA since she was 16 years old.
"That's great. I came a bit later there. I saw today a bit of her match, because she was playing against my friend. She's looking solid, so we'll see.
"It's going to be an interesting match, for sure."
