Castillo reached base all three times he batted and scored a run in Wednesday's 7-2 win over the Houston Astros.
One of four candidates to play second, Castillo walked twice and singled to the left side before scoring on a hit by Daniel Murphy, who is competing with him.
"I thought he had a good active day today, and I told him the other day I thought his energy was looking better," Mets manager Terry Collins said. "He's a little frustrated in the position he is in, and I certainly understand it, but as I told him this morning, 'You know, Luis, it is what it is, and you've got to make the most of your situation and your opportunity here."
Castillo lost the second base job last year. He is in the final season of a $25 million, four-year contract.
Winter-meeting draft selection Brad Emaus and minor leaguer Justin Turner are the other two candidates for the job, but Collins said he hopes to have the list narrowed down by early next week.
Castillo is 3-for-14 in six games with a .312 on-base percentage.
Josh Thole and Kirk Nieuwenhuis both hit two-run homers, and Thole finished 3-for-3 with two runs and a double. Murphy went 2-for-3 with two RBIs as a designated hitter.
Young struggled to get comfortable in poor mound conditions and didn't break out the split-fastball he has been working on.
"I was just trying to get a feel for the slider, fastball command, just working on some things," Young said. "There were some good things, some bad things, a lot of room for improvement, but overall I feel good."
Closer Francisco Rodriguez pitched 1 2/3 perfect innings, striking out the two batters he faced in the seventh inning.
Astros fifth starter contender Ryan Rowland-Smith gave up two runs, one hit and three walks in three innings. Jordan Lyles allowed two runs and five hits, and was the loser.
"I felt like I was battling a bit," Rowland-Smith said. "I felt great down in the bullpen. I felt on top of the ball and was staying back nicely, but I got out in the game and it took me a little bit to really lock into what I was doing.
"Overall, I was making pitches when I needed to. It's always inch by inch. I threw a lot of sliders today and hung one, which was the pitch [Thole] crushed. Overall, I was happy with the way I was battling."
Angel Sanchez went 2-for-4 with a double for the Astros.
Turner is out with a left thigh bruise, sustained when Houston's Nyjer Morgan slid into him during Tuesday's game. Collins expects him back in action Friday. ... Mets backup catcher Ronny Paulino, who has been dealing with visa issues, is expected to arrive at camp Friday. ... Willie Harris, expected to fill a bench role, is nursing a sore shoulder related to the infield practice he has been taking in addition to his regular outfield work.