Titova began skating at the age of four after her mother brought her to the rink before training with Irina Nifontova at CSKA. She trained at CSKA for four years before switching to train with Eteri Tutberidze whom asked her to leave the academy after two sessions. "I remember I went to the ice. Eteri Georgievna asked to jump a triple loop. And at that time I had no triple jumps at all – I only jumped double. Well, I under rotated it... She looked at it and immediately left... I was kicked out... Many weren't taken, they kicked them out. It turned out that in two seasons I did not jump ... Well, nothing. With what I came, with that I left."[4]
Titova later began to train with Evgeni Plushenko at the Angels of Plushenko Academy during the 2018–19 season. She began to perform triple jumps, including the triple Axel.[5][1][6]
At the 2020 Moscow Championships, Sofya won the gold medal on the junior level.[1]
Sofya competed at stages 1 and 3 of the Russian Cup, winning the gold medal in both competitions.[7] In January, she placed 8th at the 2022 Russian Junior Championships. In February, she placed 8th at the Russian Cup Final.[2]
Sofya opened her season by competing at stages 1 and 3 of the Russian Cup, winning the gold medal in both competitions. She placed 4th at the 2023 Russian Junior Championships as well as the Russian Cup Final.[2]
Sofya competed at stage 2 of the Russian Cup where she won the bronze medal. She later went onto place 10th at stage 4.[2]
In May 2024, it was announced that Titova requested to represent Armenia. The Figure Skating Federation of Russia approved her transfer request. The Armenian Figure Skating Federation has not confirmed yet the transition of Sofia Titova. "Our federation has no information on Titova's change of citizenship. We know nothing about this", said the president of the Armenian Figure Skating Federation, Melania Stepanyan.[8]
Titova's citizenship was later approved, "The issue of Titova's Armenian citizenship has been resolved. The figure skater can legally represent Armenia," the Armenian Federation said."[9]
Sofya made her debut for Armenia at the junior national championships in December 2024 where she won the gold medal.[10] She later won the bronze medal at the 2025 Volvo Open behind Kira Baranovska and Iida Karhunen.[2] Titova additonally earned her technical minimums for the upcoming Junior World Championships.[2]
At the 2025 World Junior Championships, Sofya placed 20th overall with a total score of 159.79.[11]
Titova was assigned to two competitions on the ISU Junior Grand Prix. She made her JGP debut in September in Italy finishing in 16th place overall.[12] In October she competed at the JGP in Abu Dhabi placing 24th overall.[13]