The phrase "right away at" is correct and usable in written English
It can be used to mean "immediately at". For example, "He started his task right away at 8:00 am."
They looked right away at the table.
I apologize right away at the end of the take.
It was clear right away at Thursday's Philharmonic concert, with Ivan Fischer conducting, that something special was going on.
Sometimes fund managers want to execute their trades right away; at other times, they are willing to wait for the best possible price before they deal.
You notice the women in the documentary right away (at least I enviously did), partly because of their coiled strength and confidence.
One freshman, D. J. Williams of De La Salle High in Concord, Calif., could start right away at weakside linebacker at Miami.
Locked in a Roman Catholic home for unwed mothers on the grounds of a country convent in Roscrea, Ireland, she had signed her rights away at the nuns' insistence.
At One Medical, someone answers the phone right away — even at lunchtime.
"After taking the course," she said, "I got a job right away working at a medical spa doing laser treatments".
Greece might not need to print new drachmas right away, economists at Capital Economics contended in a paper this year.
He asked the Magic to deal him right away, or at least before the March 15 trade deadline, to the Nets, the Los Angeles Lakers or the Dallas Mavericks.
