We present early science results from the First Large Absorption Survey in H I (FLASH), a spectroscopically blind survey for 21-cm absorption lines in cold hydrogen (H I) gas at cosmological distances using the Australian Square Kilometre Array Pathfinder (ASKAP). We have searched for H I 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 H I spin temperature of T spin = 100 K and source covering fraction c f = 1, the total comoving absorption path length sensitive to all Damped Lyman α Absorbers (DLAs; N HI ≥ 2 × 10 20 cm −2 ) is ∆X = 6.6 ± 0.3 (∆z = 3.7 ± 0.2) and super-DLAs (N HI ≥ 2 × 10 21 cm −2 ) is ∆X = 111 ± 6 (∆z = 63 ± 3). We estimate upper limits on the H I 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 HI = (1.2±0.1)×10 20 (T spin /100 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 HI 3 × 10 9 M ) gas disc. Such gas-rich early types are rare, but have been detected in the nearby Universe.