If white plays a game without any mistakes or blunders...

let's take time out of the equation.

white plays a solid game with no mistakes or blunders.
black plays an objectively better game.

is it possible for white to be checkmated, or will the game always end in a draw?
ie is a mistake or blunder needed for a checkmate?

maybe the answer lies in the stockfish vs lc0 matches. I don't follow them though.

I guess another question is can black force white into a position where the only moves left are mistakes or worse?
maybe like a zugzwang position, but can white end up in a zugzwang without previously making a mistake?

There are two possibilities.

Option 1 is that the starting position is zugzwang and chess is a forced win with perfect paly for black. This seems radically unlikely, but it has not been proven false.

Option 2 is that chess is either a forced draw or a forced win for white. The definition of a blunder is a move which changes the result of a game from won to drawn or lost or from drawn to lost. By that definition, white would need to blunder to be checkmated. When talking about possibilities in a perfect information game like chess, it is hard to quantify what an "objectively better game" would mean. We don't have an objective understanding of what good moves are before there are seven men left on the board, and once there are seven men on the board every known move in every position is calculated as a forced win, forced draw, or forced loss. In that situation, "better" is meaningless, as the only decision to make every move is to play perfectly (maintain the best forced result you currently have) or to blunder (play a move which forces a worse result than you have to).

Even stockfish and lc0 aren't even remotely close to telling us if chess is a win or draw for white. Vanilla stockfish is based on human heuristics (doubled pawns, piece activity, king safety) and an abridged search which necessarily misses potentially better variations in the name of speed. NNUE stockfish or lc0 are even less well understood, and they basically just play intuitively. lc0 and NNUE stockfish cannot even really explain why they think a position is good, we just happen to know they are better at evaluating positions than anything else that has come before them.

@Henryprickett : Wow, nice paragraph!

#1

"is it possible for white to be checkmated, or will the game always end in a draw?" -- No mistakes at either side = draw
"ie is a mistake or blunder needed for a checkmate?" -- Yes each decisive game contains an odd number of mistakes, at least one

"maybe the answer lies in the stockfish vs lc0 matches. I don't follow them though." Yes Stockfish vs. LC0, but also ICCF, classical World championship and other and also expert opinions of world champions and grandmasters

"can black force white into a position where the only moves left are mistakes or worse?" -- No
"can white end up in a zugzwang without previously making a mistake?" -- no

Rapid 10+0

depends on you definition of workd blunder, mistake and in accuracy. If you use the the one by lichess analysis you can be in totally losing position without mistakes.

But lc0 and stockfish matches: of course not. someone has to make mistake for win to appear.Like whole board zuzwang in A0 vs stockfish match it is obvious that stockfish had neglected importance of mobility. Just that with out silcon brain no human could have seen the build up

Chess at the highest level of play is a draw (they need to force Stockfish and LC0 to play unbalanced openings to have non-draw results); this has been known since the 1940s (Reuben Fine said the opening position in Chess is a draw back in 1942 in his classic “Chess The Easy Way”).

Now, if white opens with 1. Nh3?, Black has an edge, possibly a winning edge.

cheers. I think the consensus is a mistake or worse is needed for a decisive result. if each side makes a mistake of equal value it will be a draw.

@h2b2
The answer to your problem is First move advantage.
The retrograde analysis agrees with the first move advantage and states that 'If White plays standard game from starting position, then the game will end in victory for White only if White does not play any poor move (inaccuracy, mistake and blunder)'.
Now you would think why not draw??
Let me tell you.
Retrograde analysis states that 'Black cannot force White into a draw until White plays a poor move (inaccuracy, mistake or blunder).'
Now you would think what about zugzwang??
According to combinatorial game theory in accordance with retrograde analysis, 'With perfect play, i.e., without playing a mistake or inaccuracy or blunder, the position of zugzwang is not reachable.'

Therefore, If White plays perfectly then the game will always end in victory for White.
So, at least a poor move (inaccuracy, mistake or blunder) is required for White to draw or lose the game.

For more research, check out following links:
en.m.wikipedia.org/wiki/First-move_advantage_in_chess
en.m.wikipedia.org/wiki/Retrograde_analysis
en.m.wikipedia.org/wiki/Zugzwang
en.m.wikipedia.org/wiki/Combinatorial_game_theory

#9
First move advantage is only an advantage of 1 tempo. From gambits we know 1 pawn = 3 tempi. To win you need an advantage of 1 pawn. 1 tempo = 1/3 pawn is insufficient advantage to win the game.

Chess is a draw, but the path to the draw is wider for white and narrower for black.