Thanks for the help!

My final code:

var map = L.map('map', {
    crs: L.CRS.Simple,
    attributionControl: false
}).setView([0, 0], 2)


const path = '/chunks/{x}.{y}.png?cash={time}'

const layer = L.tileLayer(path, {
    maxNativeZoom: 1, 
    minNativeZoom: 1,
    time: 0
}).addTo(map)

function VectorToString(vector) {
    return vector.x + "." + vector.y
}

class TileHander {
    constructor(layer){
        this.layer = layer
        this.layers = {}

        this.layer.on('tileload', (tile) =>  {
            this.layers[VectorToString(tile.coords)] = tile
        })
         
        
        this.layer.on('tileunload', (tile) => {
            delete this.layers[VectorToString(tile.coords)]
        })
    }

    update(position){
        const tile = this.layers[VectorToString(position)]
        const url = L.Util.template(tile.target._url, {
            ...position,
            time: new Date().getTime()
        })
        if (!tile) return
        tile.tile.src = url
    }
}

lThanks for the help!

My final code:

var map = L.map('map', {
    crs: L.CRS.Simple,
    attributionControl: false
}).setView([0, 0], 2)


const path = '/chunks/{x}.{y}.png?cash={time}'

const layer = L.tileLayer(path, {
    maxNativeZoom: 1, 
    minNativeZoom: 1,
    time: 0
}).addTo(map)

function VectorToString(vector) {
    return vector.x + "." + vector.y
}

class TileHandler {
    constructor(layer){
        this.layer = layer
        this.layers = {}

        this.layer.on('tileload', (tile) =>  {
            this.layers[VectorToString(tile.coords)] = tile
        })
         
        
        this.layer.on('tileunload', (tile) => {
            delete this.layers[VectorToString(tile.coords)]
        })
    }

    update(position){
        const tile = this.layers[VectorToString(position)]
        const url = L.Util.template(tile.target._url, {
            ...position,
            time: new Date().getTime()
        })
        if (!tile) return
        tile.tile.src = url
    }
}