That’s one of two most common scenarios for a first LD…the other one is waking up instantly due to the incitement. In fact, I had my 9th LD last night and still I forgot I was dreaming within a minute (I was lucky to remember it again a few minutes later and became lucid again).
You may want to read this topic as ‘first aid’:
https://community.ld4all.com/t/prolonging-lucid-dreams/24077
This topic is a little bit longer to read. It’s very useful for your next step in the learning curve of lucid dreaming: Make the most out of your lucid dreams.
https://community.ld4all.com/t/dream-control-training-course/31812