Waiting for job offer letter

So it has been a week and I have been waiting for a job offer letter after receiving a verbal offer from a big tech company. How long does it usually take for a big company to send out the offer letter? I also have an offer from a smaller tech company but I asked if I can have a week to consider everything before I make a decision and they agreed to it but time is running out with them. Should I be worried? I really want to work for the bigger company but I am afraid that if something goes south with them and I decline the smaller company, I may lose out on a job.

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