"We have the big dogs in front of us, but we were the next best," said the British-born Thai, who scored a point in the Bahrain season-opener.
Former champions Williams have finished 10th and last in four of the last five seasons but, with new team boss James Vowles also bringing in fresh energy, are showing signs of stirring.
Saturday was the first time Williams had reached the top 10 shootout since Belgium last August and the highest they had qualified since George Russell's (25) freak second-place slot in Belgium in 2021.
Albon has Max Verstappen's (25) Red Bull, on pole position, and the two Mercedes, Ferraris and Aston Martins ahead of him on the grid.
In the Bahrain season opener, Albon and US rookie teammate Logan Sargeant (22) were the second most improved team, despite qualifying 15th and 16th, while in Saudi Arabia the Thai qualified 17th and Sargeant last.
"We were struggling with the tyres a lot in Jeddah, and the car was much quicker than it actually showed. We kind of left Jeddah disappointed because we felt like there was so much more potential in the car," said Albon.
"We came up with a game plan coming into this weekend and once the tyres work everything feels good...it was just one of those very smooth sessions."
The Williams driver was also impressively quick through the middle sector.
"It's the low-speed where we lose out and around here there's only two or three low-speed corners," said Albon. "So we can get away with running that low-downforce setup."
Albon started 20th in Melbourne last year but finished 10th after doing 56 laps on one set of hard tyres, a performance that saw him acclaimed by his team as a "tyre whisperer".
"We showed it last year...so why not get some more points this year?" he said.
"Aston (Martin) grabbed the headlines because obviously the jump they made is so huge, and now they are fighting for podiums every race, we're a little bit more discreet.
"We were the 10th quickest team last year. Coming into this year, on paper we are hovering around 10th and ninth but it's closed up so much now that two-tenths is putting us within the top 10.
"When you're in that position every race feels like a chance."
