Cloud functions are generally best-suited to perform just one (small) task. More often than not I come across people who want to do everything inside one cloud function. To be honest, this is also how I started developing cloud functions.
With this in mind, you should keep your cloud function code clean and small to perform just one task. Normally this would be a background task, a file or record that needs to be written somewhere, or a check that has to be performed. In this scenario, it doesn't really matter if there is a cold start penalty.
But nowadays, people, including myself, rely on cloud functions as a backend for API Gateway or Cloud Endpoints. In this scenario, the user goes to a website and the website sends a backend request to the cloud function to get some additional information. Now the cloud function acts as an API and a user is waiting for it.
Typical cold cloud function:

Typical warm cloud function:

There are several ways to cope with a cold-start problem:
- Reduce dependencies and amount of code. As I said before, cloud functions are best-suited for performing single tasks. This will reduce the overall package size that has to be loaded to a server between receiving a request and executing the code, thus speeding things up significantly.
 
- Another more hacky way is to schedule a cloud scheduler to periodically send a warmup request to your cloud function. GCP has a generous free tier, which allows for 3 schedulers and 2 million cloud function invocations (depending on resource usage). So, depending on the number of cloud functions, you could easily schedule an http-request every few seconds. For the sake of clarity, I placed a snippet below this post that deploys a cloud function and a scheduler that sends warmup requests.
 
If you think you have tweaked the cold-start problem, you could also take measures to speed up the actual runtime:
- I switched from Python to Golang, which gave me a double-digit performance increase in terms of actual runtime. Golang speed is comparable to Java or C++.
 
- Declare variables, especially GCP clients like storage, pub/sub etc., on a global level (source). This way, future invocations of your cloud function will reuse that objects.
 
- If you are performing multiple independent actions within a cloud function, you could make them asynchronous.
 
- And again, clean code and fewer dependencies also improve the runtime.
 
Snippet:
# Deploy function
gcloud functions deploy warm-function \
  --runtime=go113 \
  --entry-point=Function \
  --trigger-http \
  --project=${PROJECT_ID} \
  --region=europe-west1 \
  --timeout=5s \
  --memory=128MB
# Set IAM bindings
gcloud functions add-iam-policy-binding warm-function \
  --region=europe-west1 \
  --member=serviceAccount:${PROJECT_ID}@appspot.gserviceaccount.com \
  --role=roles/cloudfunctions.invoker
# Create scheduler
gcloud scheduler jobs create http warmup-job \
  --schedule='*/5 * * * *' \
  --uri='https://europe-west1-${PROJECT_ID}.cloudfunctions.net/warm-function' \
  --project=${PROJECT_ID} \
  --http-method=OPTIONS \
  --oidc-service-account-email=${PROJECT_ID}@appspot.gserviceaccount.com \
  --oidc-token-audience=https://europe-west1-${PROJECT_ID}.cloudfunctions.net/warm-function