Short answer: If your sampling rate is higher than your throughput, you must use some kind of polyphase decomposition of your filters to work. So if you can't do that, you can't use a 100 MHz-clockable design to filter something with a sample rate of 1000 MS/s. It's as simple as that.
However, your example is exactly the standard example of a filter that can be implemented as a polyphase decimator: you get in 1000 MS/s, you filter to 100 MHz of that, and decimate by ten (note: assuming complex sampling here). You can do that, because your bandpass restricts the bandwidth that passes through to $\frac1{10}$ of the input bandwidth.
Anyway, even so, this will very probably not work out – there's simply zero margin for "real world" effects in your 100MHz clock to produce 100 MS/s, so you should really look into a design that can work faster.
Also, it's usually not that you buy an FPGA and can say "this works at 100MHz, no matter what I do on it", but you know its maximum clocking (which typically is much higher than 100MHz for devices that can take in 1GS/s via SERDES these days), and the maximum clock rate achievable depends on the DSP you do – so you can typically just ask your FPGA design tool to generate a FIR that is optimized for high rate (rather than e.g. for low power or small ressource consumption), and you'll get a different possible rate depending on what FIR architecture you chose.
