The Eagles christened the beginning of their tenure at the Olympic Legacy Park Community Stadium with a six-try 34-24 win over Widnes Vikings on Monday in front of a sold-out reduced capacity crowd of 795.
On what the initial five-year lease at the facility can do for the club, director of rugby Aston said: “We can build.
"We can put the blocks down to make this club a viable club, a club that can generate interest, and grow the fan base again.”
He added: "The world is your oyster and you can dream the dream. If you haven’t got a dream, what have you got?”
Lloyd Roby of Widnes had the honour of scoring the first try at the Community Stadium as the visitors raced into a 12-0 lead after just eight minutes, threatening to spoil the homecoming party.
But Sheffield hit back with six unanswered tries and an Izaac Farrell penalty to earn a comfortable win, barring a late wobble which saw Widnes score twice in the final 10 minutes.
Their sixth win in 11 reduces the gap between themselves and the top six to three points with a game in hand over Barrow, who occupy the final play-off spot.
"We are capable of achieving whatever we want to achieve,” said Aston.
"Can we get top six? Yes. We have got to be consistent, we have been quite consistent, we have got to be clinical.
"Tonight we weren’t clinical enough at times, but some of the other stuff was mind-blowing.”
Aston managed to hold back the tears on what was billed as an emotional homecoming for Sheffield Eagles after nine years in exile.
In that time they have played at Owlerton Stadium – primarily a speedway track – as well as in Doncaster, Featherstone and Wakefield.
"I always said we would get back here at some stage. I didn’t realise it would take nine years, but we are here.
"There’s plenty of emotions. When I sit back and relax I’m sure that time will be a time of reflection about a job done - but started again.”