We present early science results from the First Large Absorption Survey in HI (FLASH), a spectroscopically blind survey for 21-cm absorption lines in cold hydrogen HI gas at cosmological distances using the Australian Square Kilometre Array Pathfinder (ASKAP). We have searched for HI absorption towards 1253 radio sources in the GAMA 23 field, covering redshifts between $z = 0.34$ and $0.79$ over a sky area of approximately 50 deg$^{2}$. In a purely blind search we did not obtain any detections of 21-cm absorbers above our reliability threshold. Assuming a fiducial value for the HI spin temperature of $T_{rm spin}$ = 100 K and source covering fraction $c_{rm f} = 1$, the total comoving absorption path length sensitive to all Damped Lyman $alpha$ Absorbers (DLAs; $N_{rm HI} geq 2 times 10^{20}$ cm$^{-2}$) is $Delta{X} = 6.6 pm 0.3$ ($Delta{z} = 3.7 pm 0.2$) and super-DLAs ($N_{rm HI} geq 2 times 10^{21}$ cm$^{-2}$) is $Delta{X} = 111 pm 6$ ($Delta{z} = 63 pm 3$). We estimate upper limits on the HI column density frequency distribution function that are consistent with measurements from prior surveys for redshifted optical DLAs, and nearby 21-cm emission and absorption. By cross matching our sample of radio sources with optical spectroscopic identifications of galaxies in the GAMA 23 field, we were able to detect 21-cm absorption at $z = 0.3562$ towards NVSS J224500$-$343030, with a column density of $N_{rm HI} = (1.2 pm 0.1) times 10^{20} (T_{rm spin}/100~mathrm{K})$ cm$^{-2}$. The absorber is associated with GAMA J22450.05$-$343031.7, a massive early-type galaxy at an impact parameter of 17 kpc with respect to the radio source and which may contain a massive ($M_{rm HI} gtrsim 3 times 10^{9}$ M$_{odot}$) gas disc. Such gas-rich early types are rare, but have been detected in the nearby Universe.
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