First very naive attempt at brute forcing all possible

dvd_bounce_brute_force.js

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+const { writeFileSync } = require('fs');
+
+const xMax = 1080.0;
+const yMax = 1920.0;
+
+const framesMin = 30 * 7;
+const framesMax = 30 * 60;
+
+const distanceMax = 30.0;
+
+const buffer = 50;
+
+let xStart = 0;
+let yStart = 0;
+let frames = framesMin;
+let distance = 15.0;
+let angle = 45;
+
+let angles = [ 45, 45 + 90, 45 + 180, 45 + 270];
+
+let searchHit = 1;
+
+function simulate (x, y, frames, angle, distance) {
+	for (let i = 0; i < frames; i++) {
+		x = x + distance * Math.cos(angle * Math.PI / 180.0);
+		y = y + distance * Math.sin(angle * Math.PI / 180.0);
+		if (x >= 1080.0 || x <= 0.0) {
+			angle = 180 - angle;
+		}
+		if (x >= 1080.0) x = 1080.0;
+		if (x <= 0.0) x = 0.0;
+		if (y >= 1920.0 || y <= 0.0) {
+			angle = 360 - angle;
+		}
+		if (y >= 1920.0) y = 1920.0;
+		if (y <= 0.0) y = 0.0;
+	}
+	return { x, y, angle }
+}
+
+function simulateAll () {
+	let res;
+	let attempts = 0;
+	let startTime;
+	let duration;
+	let secondsLeft;
+	for (let x = buffer; x < xMax-buffer; x++ ) {
+		for (let y = buffer; y < yMax-buffer; y++) {
+			startTime = +new Date();
+			console.time(`${x},${y}`)
+			for (let a = 0; a < 4; a++) {
+				for (let d = 0; d < 10; d++) {
+					for (let frames = framesMin; frames < framesMax + 1; frames++) {
+						angle = angles[a];
+						res = simulate(x, y, frames, angle, distance + d);
+						attempts++;
+						if (Math.abs(res.x - x) < searchHit && Math.abs(res.y - y) < searchHit && res.angle == angle) {
+							console.log(`#${attempts}`);
+							console.log(`startx = ${x} endx = ${res.x}`);
+							console.log(`starty = ${y} endy = ${res.y}`);
+							console.log(`startangle = ${angle}`);
+							console.log(`frames = ${frames}`);
+							console.log(`distance = ${distance + d}`);
+							console.log(`searchHit = ${searchHit}`);
+							console.log("++++++++++++++++++++++++++++++++++++++++");
+							return res;
+						}
+					}
+				}
+			}
+			console.timeEnd(`${x},${y}`)
+			duration = ((+new Date()) - startTime);
+			secondsLeft = (duration / 1000) * (x - (xMax - buffer)) * (y - (yMax - buffer));
+			console.log(`Minutes Left: ${Math.round(secondsLeft / 60)}`);
+		}
+	}
+}
+
+function main () {
+	let res;
+	for (let i = 0; i < 7; i++) {
+		res = simulateAll();
+		searchHit = Math.floor(searchHit / 2.0);
+		if (searchHit === 0) process.exit()
+	}
+}
+
+main();