Can I make my character a trap build when creating them in Pillars of Eternity?

As it is not possible to upgrade the attributes in game I am wondering:

Is it possible to build trap character, as in: unable to proceed during the later game, when downgrading one stat in order to max out some other?

Generally, no.

Certainly, some builds will be stronger than other, but there is very little actual content that is meaningfully gated by stats, class, or background. There is quite a bit of dialog reactivity around stats - and in some cases, you can leverage say... your high Might score to intimidate an NPC into doing what you want. But sometimes, trying to do that will backfire and start a totally unnecessary fight, closing off content.

If you're the sort of person that will get angry about dialog options not being available because of the character you rolled (Even when they almost always have no bearing on the outcomes of the dialog and simply provide flavor and style!), you'll want 15's in Int and Resolve, will want to put points in Might, and will probably not want to dump Perception. This is a tough stat spread to realistically build in many cases, and is distinctively poorly optimized. You'll also want to be either a Cleric or Paladin. You'll note that you can't be both. Even within either of those classes, you're going to have to choose an order, and some orders have more dialog than others. But they all have dialog. The point is, it's a fools errand to try to do this; build a character that fits your vision and has mechanical stats that make sense for what you want your character to do in the world - it will work out if you do that.

Mechanically, again, it's pretty hard to screw up too much, because Pillars is a party based game. Since you can fill 5 slots in your party with totally custom adventurers if need be, it's not a big deal, even if the PC you make is dead weight. And it's pretty hard to make truly dead weight, because every stat benefits every character to some extent. Maxing out Perception and Resolve on a Rogue isn't ideal - the two stats contribute absolutely bupkis to a Rogues offensive ability, and they don't really have any specialized tools or talents to make them better tanks - but a Rogue with maxed Per and Res is going to be very hard to hit, and can stand in the middle of a battlefield doing not much damage (since you presumably tanked Might... tsk tsk) for a very long time, and outlast many enemies, and shrug off friendly fire while a Wizard with tons of might blasts them to kingdom come. And sometimes, counterintuitive stat spreads can work beautifully; the classic Barbarian has high Might and Con, and Might is important for any offensive character, but in Pillars, arguably the best stat for a Barbarian is Intellect - it increases the range of their AoE and Cleave abilities, and the duration of important buffs like Frenzy.