I noticed a job opening yesterday (Thursday) that I am very excited about. The job was only posted 2 days ago. Would it be better to apply at the end of the week on Friday or at the beginning of the week on Monday?
As long as you are applying within the deadline (assuming there is one), it makes no difference on what day or at what time you apply.
The hiring manager or HR staffer collecting applications might have them sorted by date, by name, or size. There might be some sort of application software that organizes them differently. Whoever is processing them might simply pick applications at random in no discernible order. In most cases all applications are then handed to the hiring manager for review, again in a random or unpredictable order.
In short there is no way to guarantee that your application will be the first or last that someone sees but that doesn't matter anyway. Jobs aren't handed out on a first-come first-serve basis.
As Sumyrda rightly noted in the comments, one exception to that rule can be jobs in the service industry or retail that require minimal qualifications. For those jobs it's still common to apply in person and possible to get hired on the spot. When applying to those jobs you also want to avoid doing so during busy hours or near the end of their business hours.
From another perspective Alison Green over at Ask a Manager says:
Apply when it’s convenient for you to apply. What matters most is that you have an awesome, personalized cover letter and a resume that shows a track record of achievement in the thing they’re hiring for. If you have that, any halfway competent hiring manager is going to consider your application regardless of what day of the week or time of day it was received.
She summarises her advice as:
Apply as soon as you have time to do it well, and don’t worry about the timing.
If there is a closing date mentioned, then make sure you comeback before the deadline, and leave yourself enough time to jump through all the hoops. Some sites take a time to cut and paste all the required info into their profile collection system.
If there is no deadline mentioned, then apply now. Don't wait. When you go back on Saturday they may have closed the posting. they may have said once we get x number of qualified resumes we are done, and will start with the next phase.
For the larger companies once you get your info into their system, applying for another position is even easier. They ask if you want to make changes to your profile information. Take the time to review it, and make some tweaks if they are needed. You may find that it takes less than 10 minutes to apply to subsequent openings.
As long as you make it by the deadline, they generally aren't taken in order of submission, unless they receive hundreds of resumes for a single opening.
In another situation where it pays to apply early is in some civil service posts. A civil service job in the UK I applied for had (words to the effect of) in the application process:
The application deadline is September 1st. This advertisement may close earlier if sufficient applications are received