We perform a search for galaxy-galaxy strong lens systems using a convolutional neural network (CNN) applied to imaging data from the first public data release of the DECam Local Volume Exploration Survey (DELVE), which contains $∼ 520$ million astronomical sources covering $∼ 4,000$ $\mathrm{deg}^2$ of the southern sky to a $5σ$ point-source depth of $g=24.3$, $r=23.9$, $i=23.3$, and $z=22.8$ mag. Following the methodology of similar searches using DECam data, we apply color and magnitude cuts to select a catalog of $∼ 11$ million extended astronomical sources. After scoring with our CNN, the highest scoring 50,000 images were visually inspected and assigned a score on a scale from 0 (definitely not a lens) to 3 (very probable lens). We present a list of 581 strong lens candidates, 562 of which are previously unreported. We categorize our candidates using their human-assigned scores, resulting in 55 Grade A candidates, 149 Grade B candidates, and 377 Grade C candidates. We additionally highlight eight potential quadruply lensed quasars from this sample. Due to the location of our search footprint in the northern Galactic cap ($b > 10$ deg) and southern celestial hemisphere (${\rm Dec.}<0$ deg), our candidate list has little overlap with other existing ground-based searches. Where our search footprint does overlap with other searches, we find a significant number of high-quality candidates which were previously unidentified, indicating a degree of orthogonality in our methodology. We report properties of our candidates including apparent magnitude and Einstein radius estimated from the image separation.