ya you should sound the other company out, let them know them you are going to start work / accept the current offer and see if they can expedite or at least give you an update on what are the chances of getting the job.

If really cannot but they offer you a good package later then no choice just resign since you are on probation anyway and depending on your contract could be just a week's notice.

More importantly, if you manage to get the other offer as well, see which place has better prospects and career development. That should be your main priority now. Earlier on, pay should not be such an important factor, company/branding + career prospects & development should be your main concern at least for the first 2-3 years.