Previous findings show that the existence of dense cores or bulges is the prerequisite for quenching a galaxy, leading to a proposed two-step quenching scenario: compaction and quenching. In this scenario, galaxies first grow their cores to a stellar mass surface density threshold, and subsequently quenching occurs, suggesting that galaxies evolve from extended star-forming galaxies (eSFGs), through compact star-forming galaxies (cSFGs), to a quenched population. In this work, we aim at examining the possible evolutionary link between eSFGs and cSFGs by identifying the trends in star formation rate (SFR), gas-phase metallicity, and HI content, since one would naturally expect that galaxies evolve along the track of cold gas consumption and metal enhancement. We select a volume-limited sample of 15,933 galaxies with stellar mass above 10(9.5)M(circle dot) and redshift of 0.02 < z < 0.05 from the NASA Sloan Atlas catalog within the ALFALFA footprint. The cSFGs on average exhibit similar or slightly higher SFRs of similar to 0.06 dex and significantly higher gas-phase metallicity (up to 0.2 dex at low mass) with respect to the eSFGs, while the cSFGs dominate the galaxy population of the most intense star formation activities. More importantly, overall the median H I content and gas depletion time of cSFGs are about half of eSFGs. Our result supports the compaction and quenching scenario that galaxies evolve and grow their cores along the track of cold gas consumption and metal enhancement. The environments of eSFGs and cSFGs are indistinguishable, suggesting that the compaction process is independent of any environmental effects at least for the low-redshift universe.