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I wouldn't worry about your LO meeting the sitting up milestone. We would sit our little one up on our laps, on the couch, etc. But she didn't start sitting up unassisted on her own til she was about 8 months old. Which is fine.
I would just follow your LO's cues. You don't wanna rush her into anything.

Does she like sitting in a bouncer? You could feed her there in the meantime instead of a high chair maybe?

My LO was crawling before she wanted to sit up on her own! She just had no interest in doing so and it was after 6 months until she would sit on her own. But she was OK in the high chair before that.

She doesn't have reflux, does she? Baby Y was never much for sitting until right then, when he grew out of it. Until then, he looved standing all the time.

But I agree - don't worry. Most babies meet some milestones at very different paces, and lots happens developmentally between 4 and 6 months!

My lo is a little over 5 months and isn't sitting. She wants to and tries very hard, but just isn't there yet. She is still in the reclining thing in the tub. I wouldn't worry about it yet, your baby is still young.

My son is 9 months. He's been able to sit on his own since about 6 months without falling over. He still can't get to a sitting position on his own. He hasn't really tried to pull up on anything to get to a sitting or standing position. He sits in the tub and to play now, but before that I just showered or took a bath with him. Also 4.5 months is still early for solids, so I wouldn't worry about that.
They do things in their own time frame. My pediatrician hasn't had any concerns with DS growth and milestones and he's been a tad on the slow side for most of the physical ones (rolling, crawling, sitting). I'd check with your pediatrician if you are concerned though.