As written above: These are not the only two options so this is a false dilemma. Professional experience does not necessarily mean full-time job experience. You can work while studying, or have side projects in a professional environment while studying that you can showcase (i.e. contributions to open source projects or personal pet projects). That's especially true for IT. As another option, you could also do internships and have a good chance to get hired this way. If you didn't do any of that you can still state that you don't have the required experience yet and apply either way - maybe you have other positives to compensate your lack of experience. Lying is not a requirement, at least where I live.
Reading all the other comments, I have a strong feeling that there is quite some cultural differences between what I'm assuming is the USA and my personal experiences.