For real, this is not the time in its life that your plant needs a strident, doctrinal support-human! One day, but not now. Don't let the top go dry, dry- anymore. Once she's been transplanted into the bucket, (a little while) and showing comfort, then there's time and energy reserves, and you can get medieval on her ass then, not now. Remember also, that transplanting into a Grobucket that's been properly pre-moistened and prepared is important.
How I do it... not to 'Growbuckets' but to very similar SIPs, in fact, all SIPs, is the following steps in this order... (I'm not an authority, but neither can I point you to one, so I share this until I can) Fill an assembled but empty Grobucket (no water in reservoir) with already dampened* ( with light sprayed water and surfactant - last paragraph will detail more) grow matrix and pack lightly, then place an empty copy of your seedling pot in the place you wish to plant as a placeholder. Fill reservoir through fill tube and then allow 24hrs for SIP to absorb rez contents. In the meantime, if soil level drops as gravity compacts, fill with new premoistened soil*. Drop your seedling in the empty space along with whatever ritualistic majicks you feel appropriate at the time, then, tuck her in with a nice top watering (less than 2 litres/quarts aka a half gallon). Make sure there's some room in the rez before you top water this "last" time, much of it should have already been soaked up into the soil, so its not currently at capacity. It is probably best to keep rez level under 2/3-3/4 full for the first 2 weeks in order to avoid the small chance of system-over-wetness for the plant's given maturity level. This is purely precautionary, so time could be saved here in future after evidence for confidence is collected the first time around.
PS, it's not really the last time you will top water, the idea is that it is just the last time until a new state of growth has been reached in the near future, like 1-2 weeks on. My simple mind's chronically flawed yet dog-eared logic goes something like, "because I can recognize no change in a plant inside a time resolution of one week, it must take one week's worth of change, to make change." See, I told you, flawed. And yet dog-eared because thinking it has often stopped me from making multiple mistakes in quick succession. So while I know it not to be true I paradoxically believe in its power to help me grow better.
Let's pump the brakes here, however, and go back to not having transplanted yet. If you plant a too-small seedling into an overwet bucket it could set you back, or worse. Thankfully your SIP's design range suits the needs of the plant 99% of the time, and that stability allows for new efficiencies to develop. And yet because it is your first time, to innocently err out of an abundance of caution is your target result. Young plants don't do well with too much moisture, but big plants need it. Given the absence of a dry-wet "dial" on your SIP, the reservoir's state of fullness is almost the only trick up your sleeve and certainly the most effective one. Learn to use it to the best of your abilities. Meaning: Transplant into a well soaked-in planter, but one that has limited capability to make itself more so after transplant until you've stabilized the new houseguest and begun the growing trend well and for sure.
* When pre-moistening my promix (peat/perlite) I use water that has a tiny drop of dish soap to act as a surfactant, to actively reduce water's surface tension - allowing it faster, easier access into smaller spaces. Soilless mixes especially (coco or peat-based) have a chance of portions becoming hydrophobic, whereby it becomes easier for water to completely bypass large groups of particles rather than soak them. Permitting this leads to dry spots and, at best, impeded growth. Just use surfactant for pre-wetting, not for reservoir fills as the water surface tension plays an important role in the 'capillary action' and osmotic pressures crucial to making water seep upward against gravity. Surfactants do, however, make foliar sprays more effective, whether for fertilization, irrigation or pathogen control so use them there no probs, just not drip incessantly back down into soil. Some is fine, just watch for a lot of excess, a drip cloth would prevent. There are better (more easy to control/apply) surfactants than soap, brief research will point them out pretty quickly. Soap is to-hand, cheap, but requires only a tiny amount compared to normal soap uses. Be careful, suds are not desirable. Remember, only for initial dampening, and likely on recommended if you have a high peat content. Do not treat reservoir water with surfactants.