A bit ignorant la your last statement

As freshies don't choose a country, title or money as starting of career

Choose companies or industries that enable your career to GROW

Companies have to pay levies to the government for hiring (lower ranked) foreign employees. Companies have foreign worker quotas. Companies have to go through the hassle to apply work pass. Companies have to declare their percentage of foreign workforce to the government whenever they endorse an employee for PR application.

So why should a company go through all this hassle to hire you if there is ample supply of PR/SC fresh grad Engineers from local universities?

Yes, it's because you are a foreigner, inexperienced and require a special visa application. This may not be a problem for you, but are big problems for HR and employers. Also think from the perspective of the employer, not yourself, this is especially true when you answer questions in an interview.

I read on HWZ forum that some NUS grads are having difficulty getting graduate jobs. Obviously local grads in SG are more valued, which may explain why you are having difficulties. What type of engineering are you doing? From my understanding, the industry is not at its best, so graduate jobs are scarce.

If you spent the last few months looking for jobs in SG to no avail, I  would suggest you give up on SG, and apply for reputable firms in MY. Later on, when you have two years or more experience, definitely try again in Singapore.

As a recent graduate, I spent a total of two months trying to find accounting jobs in SG. I was fortunate and managed to get 3 offers from mid tiers, and 1 offer from a small company. So if you haven't even been invited for interviews in SG, move on and hunt for malaysia jobs which will be easier.