Newly-weds (less than 24 months married) don't need life insurance if they (1) both have jobs/incomes, (2) have no children, (3) have no debt, including a mortgage, (4) have a fully-funded emergency fund, (5) are young and healthy enough, (6) have low-risk livelihoods, and (7) have no other shared long-term financial obligations. Note the emphasis on "need", because some agents sell insurance as a necessity, which it isn't. The key: if one spouse could comfortably live on their own income, it is not needed. It is important to understand term life insurance as "income replacement" and be realistic about what additional help you would need were your spouse to pass away. As newly-weds in said situation, we figure the only costs we should care about in that sense are funeral costs and perhaps any related hospital bills. As it is, our emergency fund would help with that. This highlights another reason why you should have a generous emergency fund even before you consider the luxury of life insurance.
Every marriage is different though, so assess yours carefully. The 7 criteria above will be a good start. The sooner you buy insurance, the lower the premium you are likely to secure because of your age, health, and prevailing market conditions (insurability). Your insurance agent will make sure you know this fact, but don't panic: everyone will die someday (Heb.9:27), and what matters more than anything is where your soul is headed at that point. Actually I find it a little ridiculous that the life insurance calculation is basically a bet that you will both outlive your policy (or they wouldn't offer to insure you if it were more likely that you'd die within term). It makes business sense that way for the insurer. But just be objective about it, understand it, ask a ton of questions, then choose a policy that is right for you.
That said, it makes good financial sense to considered it and buy a policy no later than your second anniversary. Use the time to stabilize and understand your particular financial dynamic, build a healthy emergency fund, and prepare yourself to tackle the hard topic of death and beneficiaries. It need not be seriously emotional or morbid, but sensible.