We introduce a compressed suffix array representation that, on a text $T$ of length $n$ over an alphabet of size $σ$, can be built in $O(n)$ deterministic time, within $O(n\logσ)$ bits of working space, and counts the number of occurrences of any pattern $P$ in $T$ in time $O(|P| + \log\log_w σ)$ on a RAM machine of $w=Ω(\log n)$-bit words. This new index outperforms all the other compressed indexes that can be built in linear deterministic time, and some others. The only faster indexes can be built in linear time only in expectation, or require $Θ(n\log n)$ bits. We also show that, by using $O(n\logσ)$ bits, we can build in linear time an index that counts in time $O(|P|/\log_σn + \log n(\log\log n)^2)$, which is RAM-optimal for $w=Θ(\log n)$ and sufficiently long patterns.