World champion Evenepoel abandoned the Giro with COVID-19 on Sunday, shortly after the Belgian reclaimed top spot in the general classification with victory in a rain-affected 35-km individual time trial.
Thomas has enjoyed little luck at the Giro but he said he is keen to improve his results.
The Welshman pulled out of the Giro in 2020 after suffering a hip fracture in a crash. Three years earlier his race came to an end after he damaged his shoulder in a pile-up involving a police motorbike.
"It would be amazing to win, especially after 2020 when I thought that was it for my chance to win the Giro," Thomas, who won the 2018 Tour de France, said.
"I don't feel much pressure or expectation, but I'd love to take this opportunity.
"As you get towards the end of your career you realise how lucky you are to do this for a living and it's not going to last forever. So I'm going to make the most of it."
Thomas has a two-second lead over three-time Vuelta champion Primoz Roglic.
Following Monday's rest day, the race resumes later on Tuesday with stage 10 - a 196-km ride from Scandiano to Viareggio, which features a long climb before a fast‑running and technical descent.