Roberto Fernández struck twice inside the first 40 minutes and Dolan added a late third as Espanyol dominated from start to finish, with Levante managing barely a shot on target throughout the afternoon in Cornellà.
González was delighted with both the result and the performance his side produced in front of their own supporters.
"We're happy because it was a complicated match, which went our way early on. We were good, we controlled the game well and we had chances arriving. They created few opportunities for us. It was important to start with a win and I'm very pleased with the team's image. Sometimes we need to attack with more composure and put together more passes, so that better opportunities arrive. We had a big physical effort, but we played a great match," the coach said, according to the club's official website.
Roberto Fernández's brace, either side of a VAR check on his opener for a possible handball, took his early-season form to new heights, and González was quick to praise the striker's influence.
"With Roberto it's very easy to spot when he's in good form — when you see his pressing, you know he's got that flow. And if on top of that he starts with a goal, even better. We all need confidence and Roberto needs it too. Let's hope it lasts and that he has a great year, which would be great news for everyone."
The head coach also addressed the makeup of his midfield, with Javi Hernández and Calatrava both deployed in a role he described as demanding a specific type of player.
"It's a position that requires a certain kind of player. Sometimes it'll mean defending more. There are several players who can play there. For Javi and Calatrava it's an ideal position. We have to try to keep the ball for longer, which we did for a large part of the match. Javi has improved a lot from his loan spells, which is something I've always believed in. I want to bring through academy players, but to play in the top flight you have to pay a toll. Bauza, Hinojo, Javi and Marcos have all developed a great deal through those loans."
On the club debuts of Calatrava and Hinojo, González struck a note of encouragement.
"Cala can still give a lot more and will become more decisive. He was good, but he can give more. I trust him a lot and he'll do even better, for sure. With Hinojo we need to stay calm and be patient, because one day he'll make a mistake and we have to be there to help him."
Asked about Javier Cabrera's suspension, González voiced frustration at the disciplinary process.
"He punched the VAR screen — there was a precedent that wasn't sanctioned — and we fought the punishment right to the end. It wasn't upheld last year because of the appeals we made. It's three matches and we'll see how it's resolved. It's an automatic sanction which, in another case, wasn't punished. I don't see it as entirely normal, but that's how it is."
Looking ahead to trips against Real Madrid and Real Sociedad, González stressed the value of starting the season with three points.
"Winning is always important and helps you grow to face matches with more composure. Now we've got Madrid and Real Sociedad, which are difficult matches. If we're in good shape we can compete with anyone — that doesn't mean you're going to win. Starting like this is very good, but we have to keep pushing."
The coach also outlined his broader target for the campaign.
"There's still a lot of the league to go. What decides one objective or another depends on how you're doing at matchday 30, when there are eight games left. We'll see there. For now we need to reach 43 points as soon as possible."