There's a few reasons why this scenario wouldn't be a good fit for cloud functions, but that "couple of seconds start-up time" can be almost entirely removed from the equation by keeping the Django instance alive (all cloud function type offerings will have a concept of cold and warm starts, and some way to control persistence across calls on the same "instance").
I've run Django on AWS Lambda in a a scenario that scaled between 25-250 calls per second depending on time of day (for a runtime of 5-30 sec). Moving Django's bootstrapping so it would stay warm across calls was very easy.