You can declare your input array to be one entry wider than required. I find this often results in more readable code:
logic [N_LEVELS:0] block_inputs; // Last entry not used, optimised away
logic [N_LEVELS-1:0] block_outputs;
// Start of pipeline
assign block_inputs[0] = stage1_input;
genvar i;
generate
for (i=0; i<N_LEVELS; i++) begin: levels
some_block i_some_block (
.data (block_inputs[i]),
.result (block_outputs[i])
);
assign block_inputs[i+1] = block_outputs[i];
end
endgenerate
assign final_result = block_outputs[N_LEVELS-1];