"one of the first problems" is a correct and usable phrase in written English.
You can use it when describing something that is among the initial issues or matters to consider in a situation or event. For example: "One of the first problems we will need to address is how to pay for the new equipment."
At 3 30 a.m. yesterday, police officers at the last stop on the A train faced one of the first problems of the strike.
When Dale Vince became the chairman of Forest Green Rovers, a hundred-and-twenty-eight-year-old club in English soccer's fourth tier, in the autumn of 2010, one of the first problems that he set out to fix was on the menu.
One of the first problems that will be given to NORC will be that of cavitation.
VON RIBBENTROP: At that time the solution of the Saar question was one of the first problems up for discussion.
He built his first spectrometer there and used it to solve a chemical question for his thesis — one of the first problems solved using NMR.
One of the first problems for Tulsa developed early when the senior forward Eric Coley -- the soul of the Golden Hurricanes -- labored with early foul trouble.
This is one of the first important problems to develop a sequence-based predictor for identifying the type of a conotoxin.
One of the first-world problems most plaguing the new corporate world is the time wasted trying to find and secure a meeting room.
As an illustrative example, consider the "diet problem", one of the first modern optimization problems [ 5], studied in the 1940s: to find the cheapest combination of foods that will satisfy all the daily nutritional requirements of a person.
One of our first problems was to determine the best conducting and dielectric liquids for the REWOD application.
"One of the first signs of problems is missing lessons, so that's something teachers pick up on quickly," says Aidan Bruce, assistant principal and head of student services.
