GROTON, Conn. — Submarine maker Electric Boat has run into a challenge amid its biggest hiring push since the Cold War: finding enough qualified workers in a small state crowded with defense contractors.

To locate new employees in a region where technical schools that once offered robust preparatory trade courses have shrunk, the Groton-based division of General Dynamics Corp. collaborates with local workforce boards. It also expanded its training budget and resurrected a dormant apprentice program as it seeks to fill jobs for welders, pipe fitters and machinists.

Anne Messerschmidt, who worked retail jobs for several years, recently joined the company’s apprentice program, lured by the prospect of career advancement and higher pay. The starting wage for Electric Boat apprentices is about $21 an hour, though it varies by trade. An employee who finishes the program can make about $30 an hour, also depending on trade.

“Working retail you can’t really expand. You can’t make a life from it,” said Ms. Messerschmidt, a 25-year-old from East Haddam, Conn.

The defense industry is one of the few bright spots in Connecticut’s still-sluggish economy, which hasn’t fully recovered all the jobs it lost during the recession. Connecticut’s unemployment rate is 4.6%, down from a peak of 9.2% in February 2011, though above the national figure of 4.1% last month.

With 60,000 aerospace and defense jobs, according to 2016 data from the Aerospace Industries Association, Connecticut ranks third after Washington and Kansas among states with the highest percentage of aerospace and defense jobs in its workforce, according to a Wall Street Journal analysis.

But the state is going through hard times. It lost population three years in a row through July 2016. Economic growth has been among the slowest in the country over the past five years, ranking 44th, according to an analysis by Moody’s Investors Service. And several major employers, including Aetna Inc. and General Electric Co., are moving their headquarters out of the state in favor of big cities such as New York and Boston.

Now, the defense sector may be coming to the rescue. The other big defense companies in Connecticut— United Technologies Corp.’s Pratt & Whitney and Lockheed Martin Corp.’s Sikorsky—are also on hiring sprees, both seeking to add thousands of workers in coming years.

Behind the hiring are expectations that military spending will rise under the Trump administration.

The Senate and House Armed Services Committees announced details last week of a defense bill that calls for $700 billion in spending for the current federal fiscal year, up from the $589 billion budget in the fiscal year that ended Sept. 30. The House passed the bill Tuesday and sent it to the Senate.

The bill authorizes purchases of more than four dozen combat aircraft and repairs to the Navy destroyers USS Fitzgerald and USS John S. McCain, as well as funding for subs built by Electric Boat. A final spending plan will be included in congressional budget negotiations.

The transportation-equipment manufacturing field, which includes Pratt & Whitney and Electric Boat, employs 44,200 people in the state, up 11% since July 2014, according to the Federal Reserve Bank of St. Louis. Average wages for durable-goods manufacturing jobs in Connecticut, a category that includes many defense jobs, jumped to about $25 an hour in 2017 compared with about $21 in 2013, according to the St. Louis Fed.

New London County, where Electric Boat is based, has benefited from defense expansion, after being hit hard by the recession and the waning fortunes of the area’s casino industry, said Don Klepper-Smith, chief economist for consulting firm DataCore Partners LLC.

After years of decline and paltry growth, the region added nearly 2,000 manufacturing jobs in the two years through March, a 12% increase, according to an analysis by Mr. Klepper-Smith.

“We are now back on track in a big way,” he said.

Electric Boat’s hiring was fueled by winning a $5 billion contract for design work on the U.S. Navy’s next generation of ballistic-missile submarines and finishing up older projects. The company says it needs to hire 15,000 to 18,000 workers by 2030, while about 40% of its current employees will be eligible to retire in the next decade.

Despite the state’s economic issues, Electric Boat Chief Operating Officer Kurt Hesch said that “finding people that want to do this work” has been a challenge. “And preferably knowing they want to do it before they get here. Otherwise, you are investing in training that will not be useful.”

Among hurdles the company faces is a shortage of residents in the region with the necessary manufacturing skills. There are also fewer trade schools training people, Mr. Hesch said.

To contend with that, the company, which has been the Navy’s primary submarine maker for over 100 years, has doubled its annual training budget to $40 million and is scooping up workers trained by the Eastern Connecticut Workforce Investment Board, a nonprofit that coordinates regional training programs.

Over 4,600 people signed up for a skills and work-readiness program for the region’s unemployed or underemployed residents, said John Beauregard, chief executive of the nonprofit. About 600 completed the program and have been hired by employers, including Electric Boat. Among things the group teaches are basic skills for jobs the company seeks to fill: pipefitters, welders and machinists.

On a recent day, Michael Shell and a handful of other apprentices at Electric Boat were being trained at a center inside the company’s machine shop, practicing advanced machining techniques used to make submarine parts.

After being laid off from a local casino, Mr. Shell, a 39-year-old who served in the Marines, sought a slot in Electric Boat’s apprentice program because of the opportunity it provides for career advancement.

“I knew I would have more job security here than in the casinos,” he said.