"vast aspirations" is correct and usable in written English.
It can be used to describe someone's ambitious goals or dreams. Example: Despite growing up in a small town, Sarah had vast aspirations of becoming a successful actress in Hollywood.
Emerging from Los Angeles, a metropolis littered with vast artistic aspirations and a potent cacophony of hip-hop-slash-electronic music (or is it the other way around?), Laufer's career seems to have had a varied topography of approachability.
The Longitude Challenge prize in itself is not going to solve the entire problem, which is vast, but the aspiration is that it will provoke new teams to come up with innovative strategies.
The truth is there still remains a vast gap between aspiration and reality.
During his time among the impoverished workers there, Chen was indelibly impressed by the vast differences between the aspirations of the peasants and the harsh reality of their lives.
Because at the time the Palestinians had before them on the table, from the U.S. and Israel, a credible diplomatic alternative to war -- a peace offer that would have satisfied the vast majority of their aspirations for statehood.
An excellent fillet of brook trout is first sautéed, then covered with hazelnuts and chives, folded in half, tied with a string of budding chive, and balanced with a side of fennel and oranges — evidence of James's vast but not vulgar aspirations.
Qatar, the tiny Gulf nation that juts out into the Persian Gulf from the expanse of neighbouring Saudi Arabia, is a country of vast local and international aspirations.
It was characterised by furious Liberal Democrat outrider Lord Oakeshott as a "weak, waffly aspiration with vast wiggle-room".
My big takeaway in reading her book was that there is a vast disconnect between the aspiration of parenthood delivering true happiness and the reality of it.
