Should I use "so", "such" or "such a" in this example?

Teo has been in the US for only three years, but his teachers say he has learned to
speak perfect English in _____ short time because he’s so happy at school.

Firstly I use "such" following the structure that my textbook taught me: such + adjective + uncountable/plural noun (+ that)

I applied this structure since I thought "time" is an uncountable noun. However, apparently, the answer is "such a". Could you guys give me a hand, please?. Thank you for your support.