App Engine is a fully managed, serverless platform for developing and hosting web applications at scale. It means that you simply deploy your code, and the platform does everything else for you.
There are two types of App Engine, first is the Standard and the other is Flexible. Based on your concerns, you may need to use App Engine Flex since you can only write files to /tmp in Standard. One key advantage of a Flex environment is that you can set resource settings for it. However, you may not be able to manually provision IOPS manually and add SSD but you can set your preferred resource settings in the app.yaml. Remember that bandwidth will depend on the disk size. The higher the disk size you choose the greater the bandwidth you will have available. See this documentation for performance by disk size reference.
After setting resources in app.yaml in App Engine Flex and you still think it is not enough for your application, you may want to consider switching to Compute Engine. In Compute Engine, you can deploy instance with a high number of cores and/or increase disk size to maximize the bandwidth and there won’t be any limitation. Also, you can add an SSD in your instance to get additional boost. Additionally, I would recommend SSD persistent disk over local SSD as the data stored in local SSD persists only until the instance is stopped or deleted. For adding persistent SSD in Compute Engine, see this documentation for reference.