We don't know for sure that the universe isn't infinite, but we do know that it is at least tens of billions of light years across. We aren't going to run into actual laws of physics making growth impossible for a long fucking time.
Only provided we leave earth and we harvest energy in a more efficient way. One of the reasons I'm supportive of renewable energy is not for environmental reasons; rather, that it's energy that would otherwise have been lost. Extracting hydrocarbons removes the total amount left, but extracting energy from sunlight doesn't lower the amount of sunlight that'll be emitted. Renewables are a responsible long-term energy play, and not just for the planet's health.
Yeah sure, if we suppose that we have nearly infinite resources (energy and material and science to propel billions of humans off the Earth and across the galaxy), we have no short-term resource problem. However we're already constrained (average OECD countries energy availability has been falling since 2006), so you can't exactly hand-wave the problem away.