Despite their wealth of biological information, public sequencing databases are largely underutilized. One cannot efficiently search for a sequence of interest in these immense resources. Sophisticated computational methods such as approximate membership query data structures allow searching for fixed-length words (k-mers) in large datasets. Yet they face scalability challenges when applied to thousands of complex sequencing experiments. In this context we propose kmindex, a new approach that uses inverted indexes based on Bloom filters. Thanks to its algorithmic choices and its fine-tuned implementation, kmindex offers the possibility to index thousands of highly complex metagenomes into an index that answers sequences queries in the tenth of a second. Index construction is one order of magnitude faster than previous approaches, and query time is two orders of magnitude faster. Based on Bloom filters, kmindex achieves negligible false positive rates, below 0.01% on average. Its average false positive rate is four orders of magnitude lower than existing approaches, for similar index sizes. It has been successfully used to index 1,393 complex marine seawater metagenome samples of raw sequences from the Tara Oceans project, demonstrating its effectiveness on large and complex datasets. This level of scaling was previously unattainable. Building on the kmindex results, we provide a public web server named "Ocean Read Atlas" (ORA) at https://ocean-read-atlas.mio.osupytheas.fr/ that can answer queries against the entire Tara Oceans dataset in real-time. kmindex is open-source software available at https://github.com/tlemane/kmindex.