Having worked with GCP, Amazon, and SoftLayer/IBM over the past few years, I can say that the cost very well can be more expensive.
For example, when I was tinkering with SoftLayer, it was relatively easy to just deploy a configuration that'd easily cost me $10,000 a month if I had of been paying for it -- and that was 2x servers. Albeit, they were Quad-CPU, 1-2TB RAM, 16-24x Disks, and Dual/Redundant 10Gbps uplinks, but still -- easy to do. SoftLayer's API is a nightmare to work with though, so back to the others :-).
With DigitalOcean, you'd have to deploy quite a few Droplet's on accident to hit the $10,000/mo mark intentionally or on accident.
That said, example aside, what I would do before even choosing a provider is to map out what you think you need now, and if X, Y, Z growth goes as planned, what you should need in 6-12 months.
Why? I could tell you stay with DigitalOcean and you could, or I could tell you go with GCP and you could. But if neither can offer what you need now and should need in the future based on projected numbers and flow, you might be planning a large-scale migration from one to the next before you even get around to building out a platform to help you scale.
If you're current application state is development, figure out what you're going to need to push it in to production -- there's your base needs. When it comes to numbers, load testing will give you a general idea of what your application can take on X, Y, Z hardware (i.e. 2-12 CPU's, 2-16GB RAM, etc).
From there, you optimize your stack, retest with a new load test. Are your numbers better or worse? If better, see if there's anything else you can squeeze. If not, you know about what the max of your current hardware is and that's how you can go about scaling while keeping things affordable.
If you're numbers are worse, figure out what and re-optimize, then retest. Don't just throw hardware at something in hopes of making it better -- it won't always work.
Of course, you're also not limited to a single provider when it comes to scale. In fact, a properly ran structure would most likely scale beyond a single provider, or it should.
Relying on a single provider is like relying on a single data center when it comes to scale. You just don't do it. Too many factors at play and as the saying goes, don't put all your eggs in one basket.
If all this seems like it's too much to handle on your own, shoot me an e-mail, seriously. We can talk numbers, exchange ideas, go over what I would do with X, Y, Z, what I wouldn't do, etc. My e-mail is in my profile -- I'd be more than happy to discuss things with you. I've signed my fair share of NDA's in the past, so don't feel awkward if that happens to be the first thing you discuss with me :-).