Can I set the date for playwright browser

Way easier solution with

    page.evaluate(() => {
      Date.now = () => {
        return 1609477200000; //Jan 1, 2021
      };
    });

You can use mocking tools like TimeShift. This piece of code would inject the timeshift library and then then the date to Feb 02 2012:

const playwright = require("playwright");

(async () => {

    let removed = false;
    const browser = await playwright["chromium"].launch({headless: false});
    const page = await browser.newPage();
    await page.setContent('<a href="#" onclick="document.querySelector(\'span\').innerText = new Date().toString()">Test me</a><span></span>');
    await page.click('a');
    console.log(await page.innerText('span'));
    await page.addScriptTag({ url: 'https://cdn.jsdelivr.net/npm/timeshift-js@1.1.1/timeshift.js'});
    await page.evaluate(() => {
        Date = TimeShift.Date; 
        TimeShift.setTime(1328230923000); 
    });
    await page.click('a');
    console.log(await page.innerText('span'));
    browser.close();
})();

Output:

Fri Sep 18 2020 15:06:58 GMT-0300 (Argentina Standard Time)
Thu Feb 02 2012 22:02:03 GMT-0300

Version without tick functionality:

    page.on('load', () => {
        page.evaluate(() => {
            const OriginalDate = window.Date;

            class MockDate extends OriginalDate {
                static currentDate = '18 May 2018 12:00 UTC';
                static currentTimeStamp = (new OriginalDate(MockDate.currentDate)).getTime();

                constructor(...args) {
                    const params = (args && args.length) ? args : [MockDate.currentTimeStamp];

                    super(...params);
                }

                static [Symbol.hasInstance](instance: Date) {
                    return typeof instance.getDate === 'function';
                }

                static now() {
                    return MockDate.currentTimeStamp;
                }
            }

            window.Date = MockDate;
        });
    });

    await page.goto(yourUrl);

Version with tick:

    page.on('load', () => {
        page.evaluate(() => {
            const OriginalDate = window.Date;

            class MockDate extends OriginalDate {
                static currentDate = '18 May 2018 12:00 UTC';
                static currentTimeStamp = (new OriginalDate(MockDate.currentDate)).getTime();
                static originalNow = OriginalDate.now();

                constructor(...args) {
                    const params = (args && args.length) ? args : [(MockDate.currentTimeStamp + MockDate.getTick())];

                    super(...params);
                }

                static [Symbol.hasInstance](instance: Date) {
                    return typeof instance.getDate === 'function';
                }

                static getTick() {
                    return OriginalDate.now() - MockDate.originalNow;
                }

                static now() {
                    return MockDate.currentTimeStamp + MockDate.getTick();
                }
            }

            window.Date = MockDate;
        });
    });

    await page.goto(yourUrl);