don't know how to swim but let's breathe underwater

Some of the ways they did this were actually before marriage. We tend to call every inheritance a woman was to receive a dowry but that's incorrect, most of Austen's heroines don't have a dowry, though we know how much they'll inherit upon the death of their father and/or mother. Fortune =/= dowry. The Bennets of Pride and Prejudice, the Dashwoods of Sense and Sensibility, Anne Elliot in Persuasion, and even Emma Woodhouse in Emma all will inherit a little to a great deal of wealth but not as a dowry. This means that even Emma, who will one day have the staggering amount of thirty thousand pounds, would not be bringing wealth immediately into a marriage (though in her circumstances she has a father who would hardly let her live impoverished if she had chosen to marry a penniless man).

For women as poor as the Bennets in Pride and Prejudice (though they should've had more money each, if their parents weren't useless, as has been discussed) the distinction between dowry and eventual inheritance didn't mean much: a max of fifty pounds per annum in interest was literally less than what some servants were paid so couldn't alleviate the need for their husbands to have an independent income. But what money a woman could bring into a marriage definitely increased the likelihood of her preferences being realised. Northanger Abbey's Catherine Moreland, who "would have three thousand pounds" means she has enough of a fortune to "smooth the descent of [General Tilney's] pride" and make him consent to the marriage of his son to her. She certainly would've been glad her parents saved this money for her, instead of feeling that she was an object being bought or sold. It empowered her choices, rather than reduced them.

That the inheritance of a woman is presented as a dowry also reduces the chances a woman and the man she loves will need to wait to marry until either of them inherit something or he makes a living. If Anne Elliot of Persuasion had had a dowry, instead of a future inheritance (a "share of ten thousand pounds which must be hers hereafter"), would she have broken off that original engagement? In ch23 she tells Captain Wentworth she would've been engaged to him when he had only "a few thousand pounds" and the likelihood of more thanks to an advantageous posting. If she would receive her own few thousand pounds upon marriage would that've been enough to remain engaged from the first, and perhaps even marry once he had added a few more thousands to that instead of needing to wait for Wentworth to build their shared fortune himself?

We can also see that a dowry was an inheritance parents provided for their daughter's benefit, rather than a sale price, by how carefully marriage articles were drawn up. This could legally define pin-money (how much money a woman would receive for her private usage and upkeep from her husband), and often specified that the husband couldn't diminish the bulk sum of his wife's fortune, only use the interest it generated, so that there would always be something to support the wife and her children no matter how spendthrift he was. Think of it like an old-fashioned pre-nup or family trust.

This is a huge reason why eloping was so bad, it meant there hadn't been articles drawn up beforehand and so the legal default of 'everything the wife has is now the husband's in full' applied instead of the chance to preserve her rights to her own fortune. If Wickham had succeeded in eloping with Georgiana Darcy in Pride and Prejudice her thirty thousand pounds would've become his in full when she turned twenty-one, though her guardians could've withheld it before then, and he could've spent it all and left her penniless without legal consequence.

There are plenty of historical examples of husbands without the regulations of marriage articles squandering the fortune and selling off assets, leaving the wife eventually destitute. Marriage articles are a response to that as father's wanted to protect their daughters and her future children. It actually limited the power of a husband in favour of preserving the comforts and rights of his wife, so was opposite of misogyny (though the society and laws which required these extra protections was undeniably sexist and male-centred)

Nor was receiving an inheritance upon marriage a specifically female-only practice. Eldest sons would generally receive the bulk of their inheritance when their father died, but it was common in this time and for centuries beforehand for them to be confirmed as heir or given a set income from their father (or one of their father's lesser estates, if we're talking nobility and the ultra rich) as part of the marriage articles (which would generally benefit the wife for the remainder of her life, either as a jointure or dower). Younger sons, if not already provided for, could also be given something upon their marriage and may have a commission in the army or a church living bought for them, to give them some independence. In Sense and Sensibility, after accepting the engagement of Edward and Elinor, Mrs Ferrars gives her son ten thousand pounds "towards augmenting their income" and this allows the marriage to occur. No one accuses Mrs Ferrars of selling Edward off in matrimony, even though what she's doing is so similar to a dowry that the narration points out it's exactly what "had been given with [her daughter] Fanny".

Fortune hunters and those marrying purely for money and a comfortable lifestyle definitely existed, as they do now, but dowries were not a socially and legally mandated way to give women to men to benefit them financially. 'Mercenary' marriages were frowned upon, and women were taught to look out for fortune hunters (like Wickham). Nor was it considered only men who might marry primarily to benefit from their spouse's wealth (Charlotte Lucas being a sympathetic female example). That both men and women could have inheritances gifted upon marriage, and were represented as seeking to marry for money, helps show that the practice of dowries wasn't a sexist practice which reduces women to little more than livestock.