I've only popped seeds twice and mine did the same thing. I've read the first little leaves die off realitivly early. They are only there to provide energy during the seedling stage.
At what age is "normal" for them to die, I couldn't say. Maybe someone with more experience will chime in. Picture is blurry where the first set of leafs are but those/the stem look healthy :).
Your medium looks really moist(could just be picture). I caused root/stem rot by over watering then at young age. Could be wrong so don't take my word on it(not alot of experience) just something I noticed.
Random story, I was able to cut two seedlings at base where the rot hadn't reached and turned them into clones. Didn't think it would work being that young, it did take longer than normal for roots to show(almost 3 weeks).
Sorry if my response doesn't clearly state "yes or no" your plant is healthy. Just thought I'd share my experience.
Happy Growing :)
