Yes you can begin to apply oil-based varnish such as polyurethane on top of wood you've applied BLO to. You actually don't need to wait any time at all for the BLO to 'dry', you can begin to apply the varnish immediately without any ill effects1.
I've done this many times myself, but I should note that I am conscientious about removing excess BLO from the surface (as you're supposed to, and as modern instructions tend not to emphasise enough). Results might not be as good if you leave the surface slick with oil prior to the varnish going on; the varnish will still dry and then cure, just expect it to take longer.
However I do not have time to wait the minimum of a few days for the linseed oil to cure before applying the PU.
Bad news for you here, the varnish itself won't be ready for use within a few days. It'll take a few weeks.
Varnishes can't be relied on for waterproofing or scratch resistance until they have fully cured, and typically cure time for oil-based varnishes is given as one month2. The most you can rush this is to wait about a fortnight, but you're taking a risk and do bear in mind this is highly dependent on local conditions as well as the varnish itself of course since all varnishes don't cure at the same rate.
In addition, the finishing process alone will take longer than a few days!
You want to apply a number of coats of varnish to build up good water resistance and generally you apply one coat per day.
If you want to pare this down to the bare minimum you're still looking at at least 16 days:
- Day one you sand and oil the wood to remove the water marks, then apply the first coat of varnish.
- Day two hopefully you can apply the second coat of varnish and then comes the hard part.... waiting two weeks.
1 The oil in/on the wood and the oil within the varnish just meld together.
2 In ideal conditions. And note this is one month after the last coat is applied, not the first.