My impression is that the big road block to unlocking something like the industrial revolution is the precision of your tools. During the industrial revolution there were big advances in metal tools. Maudslay's development of a metal lathe that could be used to make metal tools was a huge step forward. I think if you can reach this point of development you should be able to make continued progress using non-fossil fuel power sources.
Are there other natural materials that could be used instead of metal to achieve this level of precision? I'm pretty skeptical on this.
Are there energy sources, other than coal, that could be used to develop early metallurgy to the point where someone could re-invent Maudslay's lathe? I suspect that there are and given enough time someone would find one. It might take longer to reach this point but I believe we could get there.