The cost of DNA sequencing has dropped exponentially over the past decade, making genomic data accessible to a growing number of scientists. In bioinformatics, localization of short DNA sequences (reads) within large genomic sequences is commonly facilitated by constructing index data structures which allow for efficient querying of substrings. Recent metagenomic classification pipelines annotate reads with taxonomic labels by analyzing their $k$-mer histograms with respect to a reference genome database. CPU-based index construction is often performed in a preprocessing phase due to the relatively high cost of building irregular data structures such as hash maps. However, the rapidly growing amount of available reference genomes establishes the need for index construction and querying at interactive speeds. In this paper, we introduce MetaCache-GPU -- an ultra-fast metagenomic short read classifier specifically tailored to fit the characteristics of CUDA-enabled accelerators. Our approach employs a novel hash table variant featuring efficient minhash fingerprinting of reads for locality-sensitive hashing and their rapid insertion using warp-aggregated operations. Our performance evaluation shows that MetaCache-GPU is able to build large reference databases in a matter of seconds, enabling instantaneous operability, while popular CPU-based tools such as Kraken2 require over an hour for index construction on the same data. In the context of an ever-growing number of reference genomes, MetaCache-GPU is the first metagenomic classifier that makes analysis pipelines with on-demand composition of large-scale reference genome sets practical. The source code is publicly available at https://github.com/muellan/metacache .