The way I see, Army Recruitment Centre (ARC) did not really give you any option to sign on other Combat vocations too (apart from ADF Infantry Leader).
I think they just not interested in you for signing Infantry or other Combat vocations due to whatever reason like oversupply of better applicants.
Have you receive your enlistment letter yet? If yes and you are going to serve SAF, you can enlist first as NSF and express your interest to your PC during BMT. Nowadays apart from S1, SAF also got para-recruitment officer (secondary appointment for regular to entertain those who wish to sign on). So your PC can link you up and recommend you Infantry EWOS if this is really what you want.
Some more during BMT, ARC will go down to BMTC and sell their opening positions which you may consider to sign on 1 of the combat vocation.
However if you have not receive your enlistment letter yet, you may post to SPF or SCDF. So if you only want SAF, you may want to consider for Supply or Transport Supervisor (Both attend the same course which allow you to re-vocation to either vocation but Transport Supervisor may help you to get free Civilian Class 3 & 4 Driving Licence) for few years (eg: 3 -5 years) before you apply for Infantry Leader. This allow you to bring your 2SG - 1SG rank over when you successfully sign on as Infantry Leader and you only needs to top up Section Leader and Platoon Sergeant Course in SCS.
Yup asked already. They said can change vocation but the chances are low and not recommended.
And for the infantry EWOS, they said that ippt gold is the basic requirement apart from education level.
Maybe now standard getting higher.