There is no "pause" feature with push subscriptions. If you can, you might consider switching to a pull subscription. Then you can control exactly when you request messages.
If you can't switch to a pull subscription, you could just return an error response when you receive messages or make your endpoint unavailable. Google Cloud Pub/Sub will backoff redelivery of messages, waiting up to 10 seconds between attempts. It will try to redeliver messages for 7 days. Depending on how long you need to pause your message consumption, this might be a viable option.
If your not going to need to switch between "paused" and "unpaused" frequently, less than once per minute, then you can accomplish this behavior by switching your subscriber to a pull subscription (and not pulling) to get the pause behavior and then switching back to a push subscription to start receiving messages again.