Atletico have won five of their first seven games and are the only unbeaten side in the top flight, while champions Real Madrid and Barca have already lost two games each.
Real Sociedad are top of the standings with 20 points while Atletico are third on 17 but have two games in hand. Real Madrid are fourth, while Barca are eighth.
"It looks like being a very close league, and whoever makes the fewest mistakes from the start could win it," Suarez said in an interview with Marca on Monday.
"From being at Barcelona I know if you start the season badly and drop points it's very hard to catch up with the leaders. If you want to win the league you have to be solid and convincing from the start.
"Things haven't gone well for Barca but we know they'll be fighting until the end. If we keep believing in ourselves and keep up this exciting start, why can't we dream of winning it?"
Suarez has helped lead Atletico's early charge with five goals since switching from Barca on a free transfer in September.
His Portuguese strike partner Joao Felix has also scored five times, hitting form after a difficult first season in Spain.
Suarez said the key to ensuring the 20-year-old continues to shine was to not hand him too much responsibility for the team's fortunes.
"Great teams are formed when every player feels equal," added Suarez.
"He is growing so much right now and with the right level of confidence can achieve great things and make the difference for us. But we need to make sure all the responsibility doesn't fall on him."