Extremely metal-poor galaxies (XMPGs), defined as having metallicities below 10% of the solar value, are considered possible local analogs to primordial systems and offer a unique window into early galaxy evolution. This study presents a large-scale search for XMPGs using data from the Dark Energy Spectroscopic Instrument Data Release 1, systematically evaluating their resemblance to high-redshift galaxies. From a parent sample of more than 14 million galaxies, we identify 662 (556 new) confirmed XMPGs and 763 (666 new) high-quality candidates via the direct Te method. Our results reveal that XMPGs follow a distinct star-forming main sequence (SFMS) that is elevated and shallower than that of the comparing star-forming galaxies. Notably, at higher stellar masses (M⋆ > 107.5 M⊙), the XMPG SFMS converges with the sequence observed in high-redshift galaxies by the James Webb Space Telescope, indicating that mature XMPGs sustain star formation rates comparable to their primordial counterparts. Furthermore, XMPGs consistently deviate below the local fundamental metallicity relation, mirroring high-redshift galaxy behavior. These findings demonstrate that XMPGs not only exhibit low metallicities but also preserve scaling relations characteristic of the early Universe, confirming their potential value as local laboratories for studying early galaxy formation processes.