Yes, different genomes can produce the same proteome.
Imagine a genome that only has a single protein-coding sequence (without splicing isoforms), the rest of the genome is simply regulatory sequences. Whatever those regulatory sequences may be, as long as that single protein is expressed, it'll be the same proteome.
If you consider a single nucleotide difference enough to say two genomes are different, then there are probably quite a lot of different genomes on earth that produce proteomes identical with at least one other genome.