According to Euronews, typically the "shaper" has been someone (I guess most common the leader) of the party that won the largest number of seats. So, making a coalition starting with a lower-ranked party would be a bit unusual, tradition-wise, but apparently not unconstitutional.
The process of forming a new government begins when all the parties have preliminary discussions to explore what combination of parties might be able to work together to reach the magic majority threshold of 76 seats in 150-seat parliament.
The lower house then appoints an "informer", who is responsible for defining the possible contours of a coalition agreement. Until 2012, this person was appointed by the King.
When it appears that a group of parties can work together, a "shaper" is appointed - almost always the person who won the election, who begins the delicate work of putting together a potential cabinet.
The parties then sign a coalition agreement and the new government presents its plans to the lower house, which then has to vote on them in a vote of confidence.
(The more official terms for those are "informateur" and "formateur".)
Also from there, the NSC did not rule out talking to the PVV, but the greens did. PVV+NSC are about 20 seats short of a majority though.
The party that might be close enough positions wise to those and apparently hasn't said much is the... VVD. But what makes that complicated is at least the fact that the current PM is the head of that party. And there might be other issues, like Wilders wanting a referendum to leave the EU. The NSC is also Eurosceptic (apparently along the PiS-Hungary lines), but doesn't quite seem to want an outright 'Nexit'.
The plot thickens however because Rutte (while still PM) is no longer party leader (of the VVD) though [apparently since August]...
Ever since Mark Rutte’s replacement as VVD leader, Dilan Yeşilgöz, indicated early in the campaign that she could potentially enter coalition talks with Wilders, the far-right leader has worked hard to look more reasonable. He diluted some of his most strident positions, particularly on Islam — such as banning mosques — saying there are bigger priorities to fix.
And Yeşilgöz is also apparently quite a bit anti-immigration, even opposing international students to a degree.
BTW, such talks can take a long time in the Dutch system. In 2017 it took 225 days to form a cabinet, and the PVV had only come in second then. Back then there was effectively a firewall formed against the PVV.
Another point of interest is 2010 when a minority government was formed [after 127 days], but with some PVV support in form of a "gedoogakkoord"--tolerance/toleration agreement--, which Wikipedia described as "a novelty in Dutch politics". (And Wikipedia lists a boatload of successively appointed "informateurs" for those negotiations.) That agreement lasted till 2012.
Time notes that's not totally unprecedented for the party that came first in the polls to not be part of the government.
In 1982, the Dutch Labor Party won the most seats, but its center-right rivals wound up at the head of the governing coalition.