Unless you present position has ample room for vertical movement, you might want to still give it a try.
Only you can weigh the value and judge the JD. As a relative green engineer, they may well want you to "assist" until you have shown your worth and then can move into more responsibility. While you state you are a Mechanical Engineer, I have no idea if you are in to Mfg, construction, design, O&G, HVAC, site, project, Bldg, or electronics industries. I also don't know it it's a local or MNC or SME company.
Favorite thing that young Aussies Civil Engineers do is to hire on at local rates plus a wee bit for housing, share a place and work at site engineers (Singaporeans HATE to get dirty or go out into the weather). Then they return home with a couple of years of international exposure and start earning close to 50% more than other of their same cohort. A couple of years of international exposure is always good on a young professionals CV. You could pull it off even easier as you also have the flexibility possibly with your parents already here.
Obviously, getting by the MOM EP hurdle is the biggest problem as you can't be bringing too much to the table at this point. But, nothing ventured, nothing gained. You don't have to quit your current job until you actually get an In Principle Approval. Once you have that, THEN leave your current employer and make your way over. If you don't get past the EP hurdle, wait a couple of years, who knows what the future holds. Good Luck.
SOME PEOPLE TRY TO TURN BACK THEIR ODOMETERS. NOT ME. I WANT PEOPLE TO KNOW WHY I LOOK THIS WAY. I'VE TRAVELED A LONG WAY, AND SOME OF THE ROADS WEREN'T PAVED. ~ Will Rogers